I'd caution to to investigate a second mortgage rather than increasing the interest rate on your current loan, since it is so low.
You'll likely be paying a higher interest rate on the second mortgage, but if it'll save you money in the long run, I'd leave the first mortgage alone.
To figure out what it will cost you, use a
loan amortization calculator and make sure that you're going to be paying less interest total with the situation that you go with. In my experience, it is very, very likely that it will be better for you just to take out a second mortgage. As I stated before, the rate might be higher, but the term of the loan will likely be shorter, and keeping the majority of the debt at a lower interest rate will likely be an advantage.
If you have already closed, don't fret - you have up to three business days to "recind" - basically, back out. You may have to pay some costs, depending on the bank or broker that you used, but hopefully they'll be able to utilize most of the things (like the appraisal) when they do the second mortgage...
Good luck!