Firstly

My teacher has said no "you or yous" in the whole of the essay.

So if I put "Keep Your Mind on the Road" as a title.. is it appropriate?
Should I put "Keep the Mind on the Road" instead?

Moreover, my friend says they are some grammar mistakes in my introductory paragraph..
I don't know what he is talking about.. can you direct me exactly where these mistakes are.

There are lucky days when a driver gets way with writing a text on a U-turn, or hearing a birthday carol from a loved one on their way to work. But not all drivers are fortunate. Ever since cell phones have existed, the numbers of fatal crashes have become directly proportional to the number of cell phone subscribers each year; whether for calling or texting cell phones are the most distracting object for a driver. While the latest hands-free phones are a safer option for some; mere visual attention is not enough. The inattention from using a cell phone causes the driver to be mentally impaired, which leads to improper driving, resulting in crashes. Consequently, distracted driving is lethal. The United States government should prohibit the use of cell phones while driving to provide more safety to the roads.

Also is my thesis and introductory paragraph good?

If your teacher says no 2nd person pronouns, then he/she means in the title, too, yes. But change that title so you don't use "the" either!!

~~~~~~~~~~~~~~~~~~~~~
There are days when a lucky driver gets away<~~Note the changes I've made in these first 9 words. Do you know why? with writing a text on a U-turn, or hearing a birthday carol from a loved one on their<~~the subject of the sentence is singular, yet this pronoun is plural; they must match; how will you do that? way to work. But not all drivers are fortunate. Ever since cell phones have existed, the numbers of fatal crashes have become directly proportional<~~that's a mathematical statement; how will you prove that? to the number of cell phone subscribers each year; whether for calling or texting<~~study comma uses in the 2nd link below; which comma use governs the need for a comma here? cell phones are the most distracting object for a driver. While the latest hands-free phones are a safer option for some;<~~study semicolon uses in the 3rd link below; what needs to happen here? mere visual attention is not enough. The inattention from using a cell phone causes the driver to be mentally impaired<~~this is pretty close to a psychological term; how will you prove this?, which leads to improper driving, resulting in crashes. Consequently, distracted driving is lethal. The United States government should prohibit the use of cell phones while driving to provide more safety to the roads. Wow! That last sentences reads funny. It sounds as if you are writing about someone's drive to provide more...!! How can you rephrase so that this misinterpretation won't be made?

http://grammar.ccc.commnet.edu/grammar/pronouns.htm

http://grammar.ccc.commnet.edu/grammar/commas.htm

http://grammar.ccc.commnet.edu/grammar/marks/semicolon.htm

... that last sentence reads ...

There are lucky days when drivers get away with writing a text on a U-turn, or hearing a birthday carol from a loved one on their way to work. But not all drivers are fortunate. Ever since cell phones have existed, the numbers of fatal crashes have become directly proportional to the number of cell phone subscribers each year; whether for calling or texting, using their cell phones is the most distracting activity for drivers. While the latest hands-free phones are a safer option for some; mere visual attention is not enough. The inattention from using the cell phone causes drivers to be mentally impaired, which leads to improper driving, resulting in crashes. Distracted driving is lethal. The United States government should prohibit the use of cell phones while driving to provide more safety to the roads.

I don't know what to do with the last sentence.

Are the days lucky? or are the drivers lucky?

Please go over EVERYTHING I wrote above. I don't reread stuff when my corrections aren't dealt with.

There are days when lucky drivers get away with writing a text on a U-turn, or hearing a birthday carol from a loved one on their way to work. But not all drivers are fortunate. Ever since cell phones have existed, statistics recorded show the numbers of fatal crashes have become directly proportional to the number of cell phone subscribers each year; whether for calling, or texting, using their cell phones is the most distracting activity for drivers. While the latest hands-free phones are a safer option for some drivers, nonetheless, only visual attention is not enough. Tests conducted by several institutes claim that using the cell phone impairs the driver's basic cognitive process. This leads to improper driving, resulting in crashes. Thus, distracted driving is lethal. The United States government should prohibit the use of cell phones while driving to provide more safety to the roads

The United States government should prohibit the use of cell phones while driving to improve road safety.

better?

No.

Start the sentence like this: In order to improve road safety ...

You still have not corrected the pronoun/antecedent or semicolon errors.

There were days when I get tired of re-using those paisley girly outfits and start to sense a mannish chic style for a day.

Firstly, if your teacher has specifically instructed you to avoid using "you or yous" in your essay, it would be more appropriate to title your essay as "Keep the Mind on the Road" rather than "Keep Your Mind on the Road." This follows the guideline to avoid direct second-person pronouns.

Regarding the grammar mistakes in your introductory paragraph, I can highlight a few areas where improvements can be made for clarity and grammar.

1. "There are lucky days when a driver gets way with writing a text on a U-turn": It seems that there might be a word missing here. It could be "gets away" instead of "gets way," which would mean that the driver successfully avoids getting caught. However, it would be more precise to rephrase this sentence to something like "There are lucky days when a driver successfully writes a text while completing a U-turn."

2. "hearing a birthday carol from a loved one on their way to work": The word "carol" typically refers to a song sung during Christmas, so it might be more appropriate to say "receiving a birthday message" instead.

3. "the numbers of fatal crashes have become directly proportional to the number of cell phone subscribers each year": This sentence can be rearranged for better clarity. For example, you could say "Each year, the number of fatal crashes has risen in direct proportion to the increase in cell phone subscribers."

4. "Whether for calling or texting cell phones are the most distracting object for a driver": Here, it would be better to break this sentence into two separate sentences for better flow. For example, "Whether it's for calling or texting, cell phones are the most distracting objects for drivers."

Now, regarding your thesis and introductory paragraph, they are generally good. Your thesis statement clearly states your viewpoint on prohibiting the use of cell phones while driving to enhance road safety. However, with the mentioned improvements to the grammar in the introductory paragraph, it would become more polished and coherent.