Women should be tested for HPV annually with your pap smear. Do it. Most people who have the low risk for cancer strains that produce warts also have the high risk strains. He has no idea if he has the high risk strain since men cannot be tested for HPV except via a biopsy of a genital wart. Get tested please. Even if the result is negative, test every year or every two years. Some women can go from being negative to positive without having sex in between. This is true because the virus levels are sometime so low that the test cannot detect it. What makes the levels high remains unclear. Some think its when a person's immune system is lower (illness, stress, pregnancy, no sleep, alcohol binges, etc).
You should assume that you have what he has or he has what you have. You cannot tell who gave it to who. It is impossible for you to not share his strain of HPV. Esp if you had unsafe sex. Getting oral HPV from performing oral sex on a man who has a visible genital wart is not as common as getting getting genital HPV but it is possible. Just because you have no warts does not mean that you don't have it too. Half of all infected people have no symptoms. When you see your dentist, have them perform an oral exam. Do this annually at the dentist to be sure there is no bumps in your mouth.
He needs to recover his health from the virus. Usually people wait 2-3-6 months before having sex after removal of a wart. Just because its gone does not mean it will not return. If you two must have sex during his recovery period, he should wear a latex condom because it will allow his body to recover. His priority right now should be his recovery. Not sex.....
After he recovers, you two can have all of the unsafe sex you want for the rest of your lives, together. You cannot re-infect each other. You cannot ping pong the virus to each other. Most people never get any more warts and remain cleared but this does not mean the virus is gone. The CDC believes that the virus remains dormant in a body forever. Stay with him forever and you will have a great sex life. If you break up, you will be left with a choice. Do you tell future partners that you had unsafe sex with a man who had visible warts which means you are infected or do you hide this fact? Most people do not say anything even if they had genital warts. This explains why 6 out of 10 sexually active adults have HPV. It is almost impossible not to get it and not to spread it. Condoms cover 50% of genital skin. The rest is exposed and prone to passing the virus. Good luck!