Can I not shower for a month?
That seems gross. Why would you not shower for a whole month?
My girlfriend hates it when I stink.
You don't sound like you treat your girlfriend well. Proper hygiene is important and it's expected that you shower daily. If you begin to small bad, she may kick you out.
I'm trying to make her angry at me.
Well she definitely will be angry at you and so will other people who have to smell you. People need to keep their body clean otherwise they will shun by others because of their stench.