I had exactly the same issue for the longest time. Every time I had a niggle I had to present to Emergencia at the clinic of my health insurer, which was usually overkill, so to speak. I couldn't work out how to find what at home we would call and think of as our GP (general practitioner)--your regular go-to person for non-urgent matters, who follows your history, approves routines examinations, and refers you on to specialists where necessary.
Eventually, I discovered that the GP-equivalent is a medico clinico. My health insurer has them physically located in the clinic itself every day (during normal business hours), or in private practice off-site, listed in the insurer's policy booklet under the medica clinica category. How to choose one (either at the clinic or in a private office offsite), I'm not sure. In my policy booklet, all the ones in private practice are listed, whereas none of those on-staff in the clinic appear on the list; the latter are kind of anonymous in that sense.
All I know is that one day not so long ago I found myself before a medica clinica at the clinic and I said I wanted a regular go-to doctor and she said she would be it. Mind you, to get an appointment with her, I have to book some weeks in advance. So when it is something short of an emergency but not able to wait too long, I guess I will still end up feeling a bit silly sitting in emergencia.