Or President Carter.
One can do a hell of a lot worse than sound like President Carter.
No it should be an adjective modifying I. An adverb would modify the verb. So “I feel bad” means your upset or sick or something. “I feel badly” means your sense of touch isn’t up to snuff.
BTW Sickly is also an adjective, but the adjective sickly refers to a chronic condition. “He was sickly as a child”
“unwell” works for me if the situation doesn’t call for more specific details about what’s wrong.
I feel like I’m fixin’ to die.
(Bolding mine.)
Got the miseries.
Feel like death eating a cracker.
Got the heebie-jeebies.
Oh. Ol’Grannys favorite Death warmed over
In Canada, it is common to say, “I fear a touch of the ague.”
Three cheers for Chefguy and your father! My mother would drill us with “nauseated is similar to poisoned, and nauseous to poisonous.”
There’s quite a bit of cross over I think:
Collapses on couch smelling of drugs, holding back of outstretched hand to forehead to brush off floppy hair
“I have a malaise!”
But, is it creepig?
That brought a tear to my eye - I haven’t heard it since my beloved mother-in-law died over thirteen years ago!
I’m glad to know that there are still a few others out there who know the difference between “nauseous” and “nauseated.” I’d resigned myself to quietly correcting it in my head when someone says they’re nauseous (or silently agreeing in some cases).
It’s funny how the impact of the phrase “I think I have a virus” has changed over the past three years, isn’t it?
“I don’t feel well.”
“I don’t feel great. I think I might be cooking something.”
In a great show of Yorkshire understatement, some of my extended family will confess to being “middlin’” when unwell. Or even “femmer” which means something akin to “fragile”.
I recall, when asking my uncle (a hill farmer) about a friend of his (who I knew was in a hospice on palliative care) his response was…
“aye, ah saw 'im thuzday and he were moderate like”
As a youngster the first time I read the Brit-version of sick to mean vomiting I was confused. What is there to clean up if you’re just sick? 
For a mild case I might say “I’m feeling *peaked.”
If it’s a little worse it’s “I got the creepin crud.”
If I’m really miserable I’ll say “I feel like I’ve been rode hard and put up wet.”
ETA: *peaked - that’s two syllables, peak-ed. I once worked with a guy who had never heard that usage before. I think he was from California, so maybe it’s a regional thing.
Why not avoid “sick” by just describing your symptoms?
The unjugged rabbitfish wasn’t “sick”, it was “coughing up blood last night”.
(M. Python reference)
But that’s my point how do I describe my symptoms? Sure I have a cough, I’m congested, there are good exact words to describe those symptoms. But that isn’t whats bugging me* its how I feel. So how do I describe that? Its feeling crappy/sick/ill (or like “sh*t warmed through”). Fatigue and lethargy is part of it but its not really describing my symptoms.
- or was, after getting steroids and antibiotics from my doctor I’m actually feel a lot better today (it seemed to be a secondary infection, I was sick, I got better but had lingering cough that turned into a whole separate illness)
‘I am not feeling at ease. I am diseased, if you will.’