Should I refinance my house to get rid of PMI? Is it a smart idea?

WE have owned the house for almost two years. We purchased for 158000 with a 30 year 3.75 interest rate. It is now worth about 200000.
We do not want to take money out, we just want to get rid of mortgage insurance which is around $180 a month.
we also wish to refinance to a shorter term, 15 year loan with 3.65 interest rate.
is this a good idea? Will we save money if we refinance or should i just stay with our current loan and make extra payments to pay off the loan sooner? But if i did this i would still be paying the PMI.

Please advice us, We are doubting our decisions.

Thank you

Read more: Should I refinance my house to get rid of PMI? Is it a smart idea?