The strong possibility also exists that his high sex drive is not associated with either of his mental illnesses. Sex drive is a biological function. It is mainly determined by chemical levels.
Should you give him another chance? That is a decision only you can make. Before deciding, consider the facts of the relationship. Those include the fact that he cheated on you and is not sure if he wants to be with you. Most people, given those facts, would not want to remain in the relationship.
Cheating is a serious thing. It destroys trust, the basis of all relationships. You must feel safe and loved in a relationship and you cannot do so if you can’t trust the person you are with. Cheating destroys trust but it does not automatically mean the end of the relationship. Trust can be rebuilt but it will take a very long time.
He cheated on you but you are essentially letting him decide if the relationship should continue. There are many men who would never cheat on their partner. It is unclear why you are allowing him to determine the fate of the relationship. What is it that you want?
If you continue to struggle with this relationship and are not sure what to do, consider consulting a therapist. Please take care.