You should be careful about using the Debt Management Companies. Most of them have non-profit status, but charge you fees for their service. The service they perform is something you can do yourself, especially since you have managed (you’ve done a great job) to keep your Credit Card payments from being delinquent.
I am concerned about the amount of debt that you owe. Is that all credit card balances..or does it include automobile balances. If you own a home, a refinance or second-mortgage home equity loan may be the best option. There are plenty of programs available even though you just started your new job and your Credit Score may be lower than it was before.
If you don’t own a home yet…then you will need to develop a plan to reduce the interest rate and monthly payments on your cards. You may be able to negotiate some reduced terms with your debtors.