That is a question that has been answered both ways. Some use the comma before the conjunction. Others say that it is not needed. I think it makes the sentence clearer to use the comma.
http://www.towson.edu/ows/sentences.htm
Yes, there should be a comma before the word "and" in this sentence. This is because the sentence contains a compound predicate, which means it has two actions (i.e., "I was only beginning high school" and "now it's coming to an end") connected by the conjunction "and." In this case, it is common to use a comma before the conjunction to clarify the separation between the two actions. Therefore, the corrected sentence would be: "It seemed like just the other day I was only beginning high school, and now it’s coming to an end."
