You can, of course. Do it! Caring for your child is the most important thing!
At the hospital, they will figure out about payment. If he doesn’t have insurance, they’ll figure out if he is eligible for insurance, like SCHIP or Medicaid. They might enroll you, too, if you have no insurance.
Even if he isn’t insurable, they’ll provide care. Worry about payment later. Hospitals usually send you a very scary bill, but if you call them, and explain your situation, they will almost always reduce the bill by a lot: perhaps a half, or even more.
But go. If your kid is sick, get care. That’s the first thing. Worry about paying later. Seeriously. In this country, health care provides must provide care, no matter what the ability of the patient is to pay.
Also, while you’re there, learn about a clinic you can be referred to for regular primary care. This is much less expensive than emergency room care. Good luck!