Before jumping to the worst conclusion, it is worth understanding what is actually driving the behavior, because it may not be what you think.
Picking fights from inside is one of the more common and counterproductive things incarcerated people do to the people they love on the outside. It is rarely about what the fight is actually about. What it is almost always about is control and anxiety. Your husband cannot see you, cannot account for where you are or what you are doing, and that helplessness builds into a kind of pressure that sometimes comes out sideways as conflict. Pushing you away is paradoxically a way of testing whether you will stay. If you stay after a fight, it answers the question he cannot ask directly.
The nurse theory and the side chick theory are possible, but they are also the product of an imagination that has been handed a lot of idle time and very little information. Inmates have all day to construct narratives about what is happening on the outside, and anxiety tends to fill in the blanks with the worst possible scenarios in both directions.
That does not mean your concerns are invalid. If there is a genuine pattern of behavior that goes beyond the typical push and pull of an incarceration relationship, trust that instinct and look at it honestly.
But if the fights feel manufactured and the accusations feel like they are coming from fear rather than evidence, that is a different situation entirely. Set your boundaries clearly, do not reward manufactured conflict with panic or guilt, and let him know that kind of behavior is not something you are going to keep absorbing.