I've been having pain in my right breast, I sleep on my right side & sometimes with a bra. No discharge through my nipple & I don't feel any lumps?

Probably OK. You have breast pain, which is a very common complaint. It can affect one or both breasts. Sometimes it is caused by fibrocystic (lumpy) breast disease. If you have large breasts, it's possible your sleep position is contributing to the pain. You should have an exam by a practitioner who really spends some time examining your breasts. A thorough breast exam takes at least 3 minutes per breast!
Right Breast Pain. It is best to get seen for this. It is more likely nothing to worry about but is worth an evaluation. Cutting down on caffeine and adding primrose oil may help. If this is the start of fibrocystic breast, the other breast will catch up and will hurt also. Remember it can be something simple like an ill fitting bra.