Best way to pay off credit card debt?

I read the sidebar about avalanche and snowball, but I am wondering some further advice as we are making payments on both the loans we have each month. I have a balance of ~$7700 on a credit card from capital one, which I've been making payments on. But the interest is almost the amount of my payments (145 interest each month compared to a $222 payment). My only other loan that we're paying off is a family loan with minimal interest ($200) per month. Together my partner and I are making around $3500 per month between our incomes but we need to make sure we have enough put aside for an upcoming dental procedure for her which costs around $4000. Besides these bills, our monthly bills are around $1900. Any advice to make progress safely here?