I have a cyst in my hand and it's very painful when i bend it and my wrist. can i just leave it alone and let it go away on its own?

Not likely: Fact it is causing pain means you are irritating it with movement (/ it irritates you as well). So short of putting wrist in cast for few weeks to allow it to quiet down...& no guarantee it won't immediately re-aggravate when resume movement of wrist...You will need to see a hand (/plastic) surgeon to have it drained (w/needle, but might recur) or formally removed.