If it's deep into the paint, you need to cut and polish. You need a good product (sorry SCA) like Meguiars and that can be expensive. It may be easier and cheaper in the long run to get a mobile car detailer. Again, m ake sure you get a detailer not just a mobile car wash guy.
Ptiiy your not closer, my son is a detailer and I get him to do mine a couple of times a year. I have learnt from him that half assed jobs or product just don't work.