Assuming the child support is being taken out "by garnishment," then generally, any other creditor seeking a garnishment gets in line. Again, generally, states set a cap on how much of a check can be garnished and most of the time, the first creditor to issue the garnishment gets the max, then when that debt is paid or the garnishment expires, the next creditor gets its garnishment put in place and so on.
Having said all that, if your check is being garnished for child support, another creditors cannot come in and take more. But, as you suspect, laws vary by state so you will want to talk to an attorney in your state to verify your risks.
You were told wrong. Although any judgment obtained in the credit card case may end up being junior to the child support order, which was pre-existing, I'm aware of nothing in Ohio law that requires other judgment creditors to get stiffed just because you have a child support order.
My strong advice is to contact a lawyer, who can file an answer to the suit. The bark of many credit card lawyers, and collection attorneys for that matter, is often worse than their bite. They make a living solely on people not responding to court summonses. If it weren't for such a thing as a default judgment, these types of lawyers would have to find another line of work. Many are sneaky too, and engage in a conversation with the pro se defendant, who calls right after being served. The conversation then leads the defendant believe they can ignore the lawsuit. Don't be a victim yourself. Contact a lawyer immediately before it's too late.