in response to TS:
it is possible to play the drums without using scores/ tabs. in fact i can't sight read to save my life. but it depends on the kind of music you're playing. most genres don't require you to use sheets at all, unless you're talking concert bands or jazz big bands. where you have to play precise and specific parts in order not to throw off the rest of the musicians. but in a small combo band, where there are usually only 3-5 people, you should not be using tabs.
one thing i disagree is that you shouldn't memorize the sheet music or anything. you should feel and remember the music in your heart not your head and let your natural groove guide what you play. every drummer has a different style and sense of groove. the original drummer for any particular rock song probably didn't have any score or tabs too. they just play what they feel is right, and as a musician (yes, drummers are musicians too) you should develop that sense of musicality too. it might not be exactly the same as that on the record, but it's alright. different people have different levels of skill, you've only played for 2 years, professional drummers out there have been playing for at least 8-10 years. so trying to play what they play might not be the way to go.
it'll be like asking a 5 year old child to read shakespeare literature. even if he can read the words, he will not be able to read it smoothly and coherently. and most importantly, in all forms of arts, he will not be able to bring out the emotions and the meaning of the literature.
so instead of focusing on what to play, focus on how YOU can bring out the emotions of the particular song, injecting YOUR own musicality and rhythming emotions into it with the limited skill you have. when you play much longer and go into deeper understanding of music as a whole, then you'll realize that you'll be able to "channel" the "spirit" of the other drummers when you play their songs. i'm not talking about spirit possession, but you'll understand when you get to that level and listen a lot, you'll actually be able to understand what other drummers are feeling, thinking, and how they interpret a certain song, and you can apply it to your own playing. this is what people mean when they ask you who your influences are. they aren't asking you what bands or drummers you like, they're asking you "who are the drummers you incorporate into your drumming, so to speak."
i hope you keep trying and don't be afraid to express yourself. this is what music is after all: expression, not imitation.
edit:
just want to add on using the analogy that Mr. Mouse used above.
music IS a language. i'll explain briefly to tie in to what i say. language is an expression. if you're hungry and you want to eat, you say the words "i'm hungry, and i want to eat". so just like in music, each note should reflect what you want to say and how you feel. hence, musical dialogue. and just like in every language, you have to understand how to read, write AND speak the language.
as mentioned, the notes are the words, musical phrases are the sentences, and the whole song is what you want to say. everybody says different things in different ways. so if one drummer is hungry, he'll say "hey let's go eat, i'm starving." another will say "i'm hungry". there is no universal sentence to express a particular emotion.
so likewise, if YOU are hungry. you won't take out a cheat sheet and read off the paper just to let others know you're hungry. you will say it YOUR way and how YOU normally say it. so as in every language, understanding the alphabets is important, but you also have to ultimately use it to express yourself.
so unless you're doing a recital, or are required to particularly play specific parts and rhythms. you should work to develop your own musical vocabulary and sentences.
