Hello girls! My son is sweating heavily, like little drops on his head…

Hello girls! My son is sweating heavily, like little drops on his head, even cold sweat. When he sucks it's normal, but sometimes just like that... He has a cough and was two months old with a smell from his head then the doctor increased the dose of vitamin D, the smell went away but the sweating is gone. But I haven't had any tests done about this, the family doctor doesn't inspire confidence saying it's due to anemia, weak immunity. Should I go to a private doctor and what tests are usually done? I give him 5 drops of childrimix and maltofer for anemia, ?