Corona of penis is sometimes reddish-purple and and sometimes itches, also dark colored skin around the corona from frenulum.what to do?

Probably not serious: If there skin flaking, sores, redness, etc, see a doctor. Most skin problems of the penis are not STDs or anything serious. Avoid using any creams, ointments, or other treatment before getting care; they can interfere with accurate diagnosis. In the meantime, don't worry. This doesn't sound serious and may not even abnormal.