Can i or should i drop my 30 year fixed mortgage to a 15 year fixed?

Can i or should i drop my 30 year fixed mortgage to a 15 year fixed?
me and my wife are in are mid 30’s we live with my mom’s the house i grow up in .my mom gave the house to us for 105,000 8 years ago i got 30 year fixed mortgage i want to refinance to a 15 year fixed with the low interest rates that are going right now should i or should i live it alone.
i got a really good rate 8 years ago. the house was appraised in the low 300’s a few years ago

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