In English, American English at least, we don't really say 'to do sport' like how it's used in Russian...like when referring to 'exercise' type activities, like: running, yoga, weight lifting, gym stuff, etc. In your example, we would just say '...he recommends I exercise 3 days a week.' Usage of sport is usually restricted to playing some kind of game/sport like soccer, basketball, tennis, etc. Swimming might be referred to as a sport if it's on a team or as part of some kind of competition or club...otherwise I'd just refer to swimming as exercise. We could say: "what sport do you like?" "did you do any sports in school," "I like playing sports," etc.

"Do sport" is wrong. "Do sports" is ok. "Do some sports" and "do a sport" are better. "Engage in sports (or 'in some sport")" is still better.

Do sport -to exercise. Do sports - football, basketball, hockey, etc.

Sports

Best: My doctor recommends that I exercise three times a week.