I've got sore feet / I've got a sore feet? Thanks.
(1) I've been walking for three hours. I've got sore feet. ---- My question is why not I've got "a" sore feet?

(2) I don't feel very well this morning. l've got "a" sore throat.

Thanks so much.

Question

I've got sore feet / I've got a sore feet? Thanks.
(1) I've been walking for three hours. I've got sore feet. ---- My question is why not I've got "a" sore feet?

(2) I don't feel very well this morning. l've got "a" sore throat.

Thanks so much.

Answer

You have either a sore foot, or (two) sore feet. 
You are forgetting about plurals. 'A' is singular. If you've been walking, both feet would probably be sore. 
You have only one throat - so 'a' sore throat is correct.