I am looking for a word that discribes this.

This makes a room messy, carries a sick person, or is another name for a lot of puppies.

http://dictionary.reference.com/browse/litter

A very messy or slovenly person

The word you are looking for is "clutter." It describes something that makes a room messy or untidy. To find this word, I suggest using a thesaurus. A thesaurus is a tool that provides synonyms and related words for a given term. You can use an online thesaurus or a physical one. Start by searching for synonyms of "messy" or "untidy" and look for words that fit the context of a room. You can also search for words related to "carrying a sick person" or "a lot of puppies." Reading through the options, you should find "clutter" as a suitable word that encompasses all the given scenarios.