I think it works just about the same as in Poland but I never heard about stiches removal in 2 months time, if it did happen, one way to go about it would be (instead of removing them yourself) to go to the emergency department and someone will help you there for sure.
Myself, I don't have or had any kind of insurance but was able to get treatment in the hospital for more than 3 days which are for free anyway even without insurance. What's over 3 days, you need a doctor to vouch/sign for you that your life could be in danger if they are to get you out of the hospital.