I would say わたしのへやはちいさいです/せまいです。. At least it should be わたしには.
いろいろなものがありません means you don't have most of things you usually have in your room. If you want to say you have few things there, あまりものがありません is used.
むこうに is more appropriate, not うしろに.
It should be きょねんの. きょねん is an adverb, so そのパソコンはきょねんたんじょうびのプレゼントで もらいました。 is OK.
わかりませんです is ungrammatical.
やきゅう means "baseball" as a game. "Baseball" as a ball used in the game is やきゅうのボール.
If this is the last sentence of your essay, it should be これが. これはわたしのへやです。 is used at the beginning of your essay, or when you show a picture of your room, and continue your essay.