The purpose of 保險 is not for 小病, it is for the case that may cause you tens of thousand dollars. Most communities in U.S have free clinics. They are usually operated by Churches or Charities. Also in most universities, there should be a student clinic which charges much less than outside clinics. Another source is State or Local Health Department. They provide medical services and charge little.
for your case, I think you need to find out how this clinic operates. Is it a charity or church clinic, or a State or Local government clinic. If it is like WIC that requires you to join a program and need State or Local government approval, you need to be careful, because this kind of service is for Citizen and PR only.