I gave my landlord rent for the month of apirl right after she gave me a thirty day notice. I found a place the next day. I want to move out now but she is refusing to give me back my money. Am I entitled to it back.

No, She gave you 30 day notice, ( I assume move out by May 1? )
So even if you were to want to move you have to give the landlord a 30 day notice, so you would owe at least though May 1st also.