Well, overly sexual does not always mean an addiction because an addiction means the euphoria/dopamine levels completely taken over one's life to the point the risks outweigh their overall health. People tend to take ridiculous risks in order to satisfy the cravings, and they do it because, like with any drug, it comforts and temporarily numbs pain (emotional, mental, and physical).

But I do think you should read this and see if it fits at all:
Causes & Risk Factors - Hypersexual Disorders

Edit: So, now that we know more to your backstory, then yes, you need to work as a team to fix this growing problem. I have a suggestion that you should schedule an appointment with a therapist so you can explore, work out, and start to heal from all the nitty-gritty parts of your past, and if she willing, you both can see someone for couples counselling. And I am glad you decided to both go to the gym together to improve yourselves in a positive manner.