You are not cheating. The important thing is that you are willing to do whatever is necessary to stay sober, even if it is taking a pill.
I felt much the same when I first got sober; angry, wanting to drink, feeling cheated out of drinking etc.. But, like you, I did not drink. My sponsor at the time always reminded me to "fake it until you make it". In other words, just go through the motions and keep doing what you are doing.
Enough time passed for me that it finally sunk in and I began to understand more about sobriety. The anger and resentment lifted and I began to slowly experience the happiness that comes from not drinking.
Do whatever you have to do to not drink. I assure you that how you feel right now is temporary. We have all been where you are and things changed for all of us.