rhytiphobia
The fear of getting wrinkles.
rare, uncountable
Now, rhytiphobia, the fear of getting wrinkles, is a phobia that I can understand. Although I have been using moisturizer on my face for years, I still have those fine and not-so-fine lines appearing.
Where it comes from
Borrowed from Ancient Greek ῥῠτῐ́ς (rhŭtĭ́s, “wrinkle”) + -phobia.
Adapted from the Wiktionary entry rhytiphobia (CC BY-SA 4.0).