Let me explain:
On a $250k purchase I can give my client a rate of 4.5-4.625% and pay just about all of h is lender closing costs. On your small loan amount the credit for the higher interest rate will not give as much of a credit as the credit is a percentage of the loan amount. So the bigger the loan amount the more credit you will get and the lower your total fees will be. If you are going to have the loan for a long time it may make sense to go with a lower rate like 4.25% and pay slightly higher fees. This is the current rate for a 30 year mortgage with my different lenders I use as a mortgage broker.
In your case because of the small loan the rate will be higher. If you are still paying the mortgage insurance and if the home can appraise for enough you may be able to drop the MI by contacting the lender and asking what the procedure is.
Honestly if your rate is not through the roof it may not even make sense to refinance it depending on the closing costs... on a loan that small dropping 2% points will not make a huge difference so you really do need to look at the total costs and see how many months or years it will take to recoup the closing costs. A good broker will do that for you and it is easy to figure out on your own as well.
As a Realtor I do not originate FHA but I work with a lof of good lenders that I can point you to if you are interested in refinancing and seeing it makes sense.
Good luck to you.