Sounds like you're doing well at 4 months!

There are many causes of dry mouth, including from radiation/chemo we're used to hearing about, but other causes can be from dehydration, medications, illness, exercise, etc. I'm not sure of your liquid intake, and varying needs, which can include the elevation you're at, temperature, activity level. Some medications can also cause dry mouth, and illnesses like diabetes, kidney malfunction, hypothyroidism are some too, even exercising, and mainly breathing through your mouth, can cause dry mouth, as well as sleeping with your mouth open if that is happening. which can be some things to look into on your own, with your medical team.

I always thought that too much exercise lowered your immune system, and moderate exercise helped to protect it, and probably read such many years ago, but it never changed my habits, and dealt with the frequent colds back in the day. Adequate sleep, rest, proper nutrition, avoiding/protecting against illness, can also help your immune system.

I hope this helps.