There are different ways to describe feeling ill:

1) noun + problem
2) feel + (adjective)
3) I’m …ing
4) I can’t / won’t stop …ing
5) I’m unable to (I can’t)…
6) I have + (noun) (*important note)

Noun + Problem

My head hurts
My tooth hurts
My lower leg is swollen
My stomach aches

Feel + Adjective

I feel sick
I fell dizzy
I feel bloated

I’m …ing

I’m vomiting every morning
I’m coughing up blood

I can’t / won’t stop…ing

I can’t stop coughing
My hand won’t stop shaking
I can’t stop going to the bathroom
I can’t stop being sick

I’m unable to
…/ I can’t….

I’m unable to swallow
I’m unable to sleep
I can’t breathe

I have a + noun

I have a sore head
I have a broken leg
I have a toothache
I have a pain in my side

Sore vs. …ache vs. have a pain in the…

You can always use sore.
However, some parts of the body have ‘…ache’
‘A pain in my…’ is used for general areas of the body

a sore tooth
a sore ear
a sore stomach
a sore head
a sore toe
a sore nose

special areas that take …ache:
toothache
earache
stomachache
headache

I have a pain in my side
I have a pain in my leg
I have a pain in my stomache

Important Note

If the part of the body is usually described as ‘sore/…ache’, using ‘a pain in my…’ is unusual and so has a different meaning (maybe you have no idea what the problem is, or the problem has not gone away).

– examples

‘I have a stomachache’ (usually a short term problem)
‘I have a pain in my stomach’ (unusual, maybe more severe (not a normal problem))

‘I have a sore leg’ (my leg hurts)
‘I have a pain in my leg’ (not sure why, could be more serious)