Not in this case. The yr/y/'r is not always translated between Welsh and English, particularly with names of things, including some diseases, some countries and some specific events. For example:
- yr Almaen, y Swistir, yr Aifft - Germany, Switzerland, Egypt
- y ddannoedd, y diciáu - toothache, tuberculosis
- y Pasg, y Nadolig - Easter, Christmas
- y Bala, y Rhyl, y Fenni, y Barri, y Bontfaen - Bala, Rhyl, Abergavenny, Barry, Cowbridge (names of towns)
Sometimes the y/yr is dropped in informal usage, though.
As is well explained above. Therefore 'Toothache' (without the definite article in English) is 'Y Ddannoedd' (with the definite article in Welsh)
Depending on context the English might use the definite article - for example 'the toothache is terrible but the earache is worse' or 'the toothache is terrible although the swelling has gone down'; but also: 'toothache is terrible and so is earache'.
I agree wholeheartedly, Ffwlbart. "Toothache is awful" would be used when talking about the general condition, but when talking about a specific case, it would be "the toothache is awful", therefore both translations should be accepted.