Hi there,
This drug is usually prescribed for ADD. Read here :
http://www.rxlist.com/dexedrine-drug.htm
for side effects. You'll note the central nervous system is stimulated but lower down on the page you'll see it actually causes impotence.
You say he doesn't cheat per se but later you say he has cheated. It's pretty clear that he is cheating really. It has nothing to do with job stress etc. He wants to play around, it's that simple. What causes that drive does not matter as it is part of him. You must decide if you will tolerate it or not.
I think your boyfriend has some deep seeded issues regarding women and sex. He does need psychiatric help. I know it's diffuclt to realize, but he is cheating on you, and I don't think I would be involved with this man, one woman will never be enough for him. The drugs he is taking normally hampers the sex drive, I've never heard of the opposite happening. Plus, keep in mind that life is always full of stress and if this is how he handles it...don't you deserve more out of a man? Fidelity is not asking for too much, with men like this, it will never happen. I have a girlfriend who has been in therapy for the same problem for over 20 years, still she does this and cannot maintain a long term relationship.
That medication is a stimulant and it could push someone into mania which causes a lack of judgment. He should speak to his psychiatrist about that and let them know what is going on and it would be best to encourage him to do that. The relationship issue is another aspect but that may be one cause.