Tricky one, isn't it? When I was working as a professional performer, I tended to call myself an "entertainer" rather than musician because, the musos around me were all so much more capable, and I felt inadequate to claim the title. However, thinking back, this is actually pretty elitist: surely anyone who can make music at whatever level is a musician?

And, as for reading the "dots", that's just one small aspect of being a musician and I wouldn't say it was an essential one (presume no-one asked Ray Charles or Stevie Wonder if they could read).