Hi, You said you don't see a point to see a doctor but actually there is. Doctors has accesses to test and also can help find out what condition/disease/etc you have. I think it up to you to find out if that conditions/diseases/etc is the cause of your odor. For example, I have gone to the doctor but never told him about my odor problem and i don't intend to anytime soon. What i found out Is that i have diverticulosis and recently they got inflamed (diverticulitis). I have external and two internal hemorrhoid and a few Polyps. you may wonder what does this have to do with anything. Well, the the food i ate and my non active lifestyle cause theses problem in my colon and rectum area. and it also contributed to my b.o. Conclusion, if i have not gone to the doctor i would not have known about all this helpful information.
Also, you don't have to go to a gym to exercise. you can do it in your own home without equipment. Things you can do: Run in place, push up, sit up, dancing, walk around the block, etc. be creative!
What do you mean your diet is good? Did you cut out all process and junk food? do you eat lots of veggies and fruit? drink lots of water? I know it hard to cut out all the food you love eating but we must make those sacrifices Anyways, Good luck for now!