I don't have credit
You certaintly have my sympathy. I had some friend with same problem when they was teens. I have a hard time imaginng that surgery would only cost 3000. That would be cheap in America. Your self image is not allowing you to date girls. I have seen many young men with the same problem. Some are very sensitive about it and some don't show no negative emotions. I highly recommend you seek counseling about it.
Getting Care Credit is pretty tough with no credit history and only $700/month income. (I work in a medical office and see people get declined all the time).
If you live at home with your parents, just save your money for 4-5 months and pay cash.
forget Care Credit. Save up your money or discuss a loan with your parents.
ask the surgeon if they have financing