1. Maybe things didn't go well at work.
2. Maybe situation didn't go well at work.
----------------------
(Does things' mean 'situation' here?)
3. You'll feel better.
4. You'll feel good.
5. You'll feel better.
6. You'll feel well.
7. You'll feel healthier.
8. You'll feel healthy.
-----------------------
(Is 'better' from 'well' or 'good'?)
In a way, 1 and 2 mean the same. "things" is general. "situation" is specific. What situation? So they don't really mean the same thing.
"better" is a relative term. One can feel "better" than one did before, but still not feel "good" or "well" or "healthy". After the first three days of a cold, we usually begin to feel better; the symptoms are less severe. That does not mean we are "over" the cold yet or feeling "good" or "well" or "healthy".