Yes, that is right, in theory. BUUUT, while your dentist is correct that your gums are inflamed, it's *likely* not from his (I assume it's his) "gingivitis" diagnosis. Gingivitis, a bacteria, is almost always due to plaque, so unless you've been really neglecting your teeth, cortisol is causing it.
Your gums are inflamed because they're part of the body's soft tissue, which gets inflamed due to cortisol, the major stress hormone.
If you brush your teeth attempting to get rid of something that's not there, you're going to wear them away further.