If you get $1500 per month, and $500 is supposed to be principal, then you are receiving $1000 per month, or $12k per year of interest income. You should be filing a tax return. Check with the bank holding the trust to see if the trust is paying the tax. IT would be better for you to pay it, because it seems like you would be in a low tax bracket.
Have you made any improvements to the house over and above the $100k that your grandmother paid for? Did you make any downpayment on the purchase? Or did your grandmother finance 100% of it? If you paid $345k for the house, your basis is $345k, less the amount of debt forgiven. If you did not make any improvements to the house, and your basis is the $345k, and you never made any payments on the mortgage and your grandmother did not gift you your annual amount, your basis is $345k cost less $345k debt forgiven, for $0 basis. If you sold the house for the $623,726, less the $250k principal residence exclusion, your gain would be $373,726. Long Term Capital Gains are taxed at 15%, so your tax bill would be $56,059 from this transaction. Your actual tax bill might be more or less, depending on if you had any other income.
Did your grandmother by any chance gift you the $14k per year that is allowed without filing any paperwork? If she did, for example, your gifts would have reduced the debt by $210k. If the original mortgage balance were $345k, less the $210k of gifted payments, the COD would be only $135k. Your basis would be $345k - $135k debt forgiven = $210k. If you sold it for $624k, less the $210k basis, less the $250k principal residence exclusion, your gain would only be $164k. Tax on this at 15% is $24,600.
Any other payments to your grandmother, or any improvements that you made, would reduce this gain.
I hope this helps! Please let me know if you have any more questions.