It's good you're wondering about that. There is some debate but my understanding is that birth control pills cause some liver damage (i was on bcp for a year and stopped taking them because I was really upset by the information I found about them).
Basically, they work because they alter the hormone balance in your system. But this also means that you have extra hormones in your system that your body is incapable of handling 100%. Your liver and your spleen, which are the two most affected organs when you have mono, filter your blood for viruses, infections, and anything else that shouldn't be there, included excessive hormones that are not naturally produced by your body.
There is a minimal risk taking bcp, otherwise, all the women who take it probably wouldn't be taking it. However, after having mono, you need to make sure that your liver and spleen are in good condition. If your immune system (lymph nodes, liver, spleen) are not in good condition after mono, you can get it again, and again, and again, leading to chronic mono and sometimes chronic fatigue syndrome.
The best thing to do would be to go to a vitamin store, health food store or you grocery store pharmacy/vitamin section and look for milk thistle. This is one of **the best** way to detox/cleanse your liver and get it strengthened and working right.