Don't do it. Not yet at least. If your divorce is only a few months old, likely the child support order is also a few months old. You should have stated all your outlying debt during the child support calculation part of the process.

Child support can only be modified if there is a period of time that passes (usually 1-2 years, depending on state that the divorce was ruled in), or extraneous circumstances (loss of job, disability).

You say you have legal fees. You don't need to pay them in full if you have not already. If you have, you're out of luck. If not, work with your current lawyer. I'd advise not to switch lawyers right away. What you get with one, you'll likely get with another. Avoid court if you can. With divorce, it makes total financial sense for lawyers to keep the grist mill well oiled with family strife.

Life does get better. Pay minimal towards medical bills. Call them, and work with them. For CC debt, for now...pay minimum to keep interest at bay. Right now you might feel like you are in a negative cash flow state, but you're employed and with two jobs as well. This is your bottom of the barrel moment. Only way to go is up, and that will just take time and effort.