Hi Patti! OK, the issue is — they’re both right! It all depends on what we’re trying to say … and how strict we are with what they’re supposed to mean.
To say we feel well is meant to be about our health, as you mentioned. Usually when we say we feel good, we mean our spirits are high, although . . . it can also mean we feel healthy.
I’m not a purist with those two, although many are. And to say “I feel well” may strike others as odd. It just doesn’t quite sound right! So in very casual conversations, I usually stick with good.
Don’t know if this helps, because language continues to evolve, and none of us are ever in the same place with every change that comes along!