We are self employed as well, but your options really depends on what state you live in.
If your gross income is below 200% of the poverty line (not the same amount $ depending on the States), your child could qualify for your State's health insurance. For example, where I live in NC: family of 5 is about $54,000/year. Everything would be covered and the copay ranges from $1 up to $5.
If state insurance is not an option, get some free quotes to see what is out there. You need a company that has an A rating. Do not settle for a B rating in order to save a couple dollars. Be aware of waiting period for treatment and any pre-existing condition policy.
Hopefully, more will come with more advise! Welcome!