I would really caution against trying to hide marks or lie about them to your doctor. Anything you tell them about your sex life and interests is confidential and they could be in HUGE trouble for breaking that.
However, if you lie and say you fell down and they know it's not the truth they may think it's abuse. If that's the case then they have a legal obligation to report it to the police.
The few moments of embarrassment in explaining to your doctor why you have marks would be far better than the embarrassment of a visit by the police.