Spirits don't get viruses or develop diseases. When a spirit is "sick" it is for the same reasons our energy can become unhealthy. Either the energy is damaged or there is an imbalance. You are feeling ill because of your connection to her. You're empathy is picking up on her condition and how it feels to her.
You can heal a spirit much like you would heal your own aura. But you must be gentle. You can also cast a healing spell on her as you would for a physical person. Since she doesn't have a physical body, the magick will work like it does in works of fiction...she should be instantly better.
IF she does not seem to be recovering, she may unfortunately be scarred. And that makes sense as to why she is using your energy (spirits don't need to absorb energy around them to remain "normal" unless severely damaged). That means mental and/or emotional damages are so great that its going to be a lot more work involved to help her. When a woman is raped, it takes a lot of work to help her heal. It would take months if not years to fully recover. When a spirit is scarred, their emotions and mental state have a lot of influence on their overall health.
Good luck. I find it refreshing to see someone here who works with spirits, sees them as people and wants to help them.