Looking on the internet deeply has found these results:

i am sick is the most popular phrase on the web.

I am not feeling well 1632,000 results on the web	i am sick 14,910,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
«I would like some advice from you, because I am not feeling very well. I am in distress and I have even thought about suicide. 'Cause I am not feeling well. How can I act like I am not feeling well when I am feeling well. I am afraid he's not feeling well. That's why I'm covering his class today. I am not feeling well today. Call the army, I am not feeling very well. I want to continue speaking, it is just that I am not feeling well. Do you even care that I am not feeling well?	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

I am not feeling well

1632,000 results on the web

i am sick

14,910,000 results on the web

More popular!

«I would like some advice from you, because I am not feeling very well. I am in distress and I have even thought about suicide.
'Cause I am not feeling well.
How can I act like I am not feeling well when I am feeling well.
I am afraid he's not feeling well. That's why I'm covering his class today.
I am not feeling well today.
Call the army, I am not feeling very well.
I want to continue speaking, it is just that I am not feeling well.
Do you even care that I am not feeling well?

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.