Do I have to pay my real estate agent twice for selling my house and for her finding me a new house?

The answer to this question varies from state to state depending on the terms of the transaction. But in general, the seller pays the real estate commission.

The seller will pay his listing agents fee and the buyers agents fee. Commission varies from state to state, in Arizona it's 6%. 3% goes to listing agent and 3% goes to the buyer's agent who finds a buyer for your home. If your agent also helps you find a replacement home the listing agency will pay your agent because you are a buyer working with a buyer's agent at

 this point. In Arizona buyer's representation if “FREE” the seller of the home you find will 

pay your agents commission.  I hope this clarifies your question.