"What disease do I have?"
Translation:Cén galar atá orm?
The explanation of Cad é an t-am é? being defined as “which” on the Gramadach na Gaeilge site is explained by looking at the original German-language version of that page here — the Irish question is translated into German as Welche Zeit ist es?, and welche is German for “which”. This is an example of an Irish → German → English translation that doesn’t match an Irish → English translation.
Only one use of cad é for English “which” is identified in the NEID, in the sense of “the particular one/ones of” — for example, it shows “tell me which days you’re free” as being translatable to abair liom cad iad na laethanta a bhfuil tú saor. The “asking for identification, selection” sense of “which” (definition #5 on the NEID page) only offers cén and cé acu as translations, which is the sense that the sentence in this exercise would need.