credit card transfer

I’m pretty close to the maximum limit on my credit card (I owe $7,200 and the limit is $7,500). I’ve already cut up the card and changed my spending habits and I’m pace to pay it off over the next 12-18 months. Problem is, the interest is killing me. If I pay the minimum monthly balance of $300 then the next month I get charged $200 in interest, so my monthly payments are barely chipping away at the balance. Is it smart to apply for a new card with zero interest on balance transfers and transfer my balance? If I could get 12 months of no interest then I could bring the balance down significantly and get close to zero, but I hear that doing this affects my credit score, at least during the short term. Should I stick with my card?