Just like "I have a headache."... I would say "I have a toothache". Is it common to say, "I have toothache" in Britain?
If I had more than one tooth hurting, I would probably say "my teeth ache" this sentence confuses me also. Is this sentence about teeth hurting in general, because it's plural?
It's not plural, although it looks confusing at first sight. As @ibisc says above: "teeth" is dannedd, "toothache" is y dannoedd. The phrase in Welsh could refer to one or more teeth.
This sentence in first place seems to mean "I have the teeth." I am wondering why toothache is constructed in another way than all the other health complications from this lection. You should expect "daint tost". Does this exist also? Could you construct the others also this way like: "Mae'r ben arna i." for "I have a headache."?