Cheers
If your mortgage interest is still sufficiently high that you're reporting it on Schedule A then a HELOC would probably be the right answer. However, the first thing to do is work out repayment terms with the doctor and hospital and see what your insurance will cover (a $200K+ house suggests you likely have a job that provides insurance).
i would probably take the home equity line of credit.
if you refinance, you're typically looking at a 30 year mortgage - though some of them will look at a 15 year one.
take the line of credit for as little as you can (so the $20K you need, but not more), and then make payments to it.
refinancing in this market isn't very safe right now. because the bank you refinance with may not be the one that continues to carry your loan.
a recommendation - you might want to look into BECU, if you can join it - i know in WA state, anyone can join, but i don't know where you are.
It probably makes sense for you to do a refinance if you're pretty certain about staying in the home for 5-8 years. You'll save almost a full percent interest on the $125k loan balance, plus the extra $20k that you borrow will be at the 5.0% rate also. If you take a HELOC you'll probably pay closer to 7% on the extra $20k. The interest you save will probably make up for the closing costs before you move.
Although, before you borrow against your home, I would suggest you talk to the medical provider about setting up payments on the medical bills. Medical bills are typically interest free if you set up payments. That way you don't set yourself back on paying off your house.
Talk to your lender and see if you can refinance without paying any fees. If they want to charge you then go with the equity loan.
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