No, your PMI does not get refunded. That is similar to asking your car insurance company to refund your premium if you do not have any claims in your coverage period, not going to happen.
There is probably going to be some sort of pre-payment penalty if you refinance this FHA loan, check on that as well.
You may be able to refinance through your current lender, but bear in mind each refinance is going to cost you whether you use your current lender or not. There may not be upfront costs, they will roll them into the loan, but there are going to be costs.
You are going to have to weigh the possible pre-payment penalty, the cost of the refinance, and any change of interest rate against what you are going to pay in PMI. It may benefit you to pay the PMI (which is also a tax write-off as well).