I have seen moist used often in this context.
"My eyes become moist as I hold back my tears."
1.1 (of the eyes) wet with tears.
‘her brother's eyes became moist’
Another word used often in this context is (quite literally as used in the question itself), watery.
"My eyes become watery as I hold back my tears."
1.1 (of a person's eyes) full of tears.
‘My eyes were a bit watery, something that happens after anyone shouts
With some rearrangement of words, you can also use the verb well.
"My eyes welled with tears as I tried to hold them back."
[often well up]
1 [no object, with adverbial (of a liquid)] rise up to the surface and spill or be about to spill.
‘tears were beginning to well up in her eyes’
‘His eyes welled with tears as they rushed down his cheeks like