what if my house appraises higher than the accepted offer?

This would be a happy day for the buyer. Nothing you can do after you accepted the offer. Sorry

Most likely nothing. Once you get to the appraisal, most likely all cancellation clauses have expired. Please know that appraisals are very subjective and not perfectly accurate. Appraisers have the leeway to plus or minus the various features of your home based on comparable homes. It can be all over the board.

I am sorry to hear that your agent was awful. In Texas, the seller typically does not receive a copy of the appraisal report so you would not necessarily know if the home appraised higher than the sales price. It will not change the contract price if it comes in high. If the appraisal comes in low, you would be informed and in that case things may need to be renegotiated. Again, this is Texas real estate, but I assume that it is probably similar everywhere in this regard.

I am licensed in Texas so I am answering your question based off of Texas rules. If the home you are selling appraises for higher than the offer you accepted there is nothing you can do. You can not cancel the contract that you have already agreed to or the purchase price. Unfortunately, it would be money you left on the table so to speak.