Can I refi?

A refinance may be a possibility, particularly since Zillow has not proven to be an accurate representation of value.  If your first mortgage is currently owned by Fannie Mae or Freddie Mac (which you can determine by going to Fannie Mae or freddie Mac web sites  ) you may be eligible for a Fannie Mae "DU Refi Plus" or a Freddie Mac "LP Open Access" refinance.  Those programs allow you to refinance you current mortgage up to 95%-105% of appraised value, depending on the originating lender.  My company only allows 95% on the first mortgage.  That means that if you currently owe 128,000 on the first mortgage and you want to do the new mortgage at lets say 135,000 to pay for your closing costs and prepaid expenses, then we would need the home to appraise at 142,105.  Some lenders may be able to accomplish the same loan with an appraised value of 128,000.  Your second mortgage would have to  willing to sign a Subordination Agreement which means that they agree to remain in a second lien position behind the new first mortgage. 

If the 117,000 is an accurate value and you would not have the capacity to pay the first mortgage down to that level, then a modification would be the only way to reduce your rate and/or payment.  There is no reason a modification should harm your credit.  There have been reports of lenders reporting derogatory credit when you enter the 3 month trial period, but they should be reporting those reduced payments as Paid As Agreed and it should not negatively impact your credit score.