I have dreaded aging, aged, and now I suppose I dread the fact that I have aged, lol. It's probably not quite the same for men, seeing your reference to losing "cuteness," but I think it's similar. An image I always had was that aging was locking me out of certain paths I could take, narrowing the path of where my life would end up. You can tell me if I'm wrong, but I feel like that's similar with the cuteness concern, right? Attractiveness opens doors; it gives you a moment-to-moment advantage in most interactions.
As I said, I haven't really gotten over aging. But one thing I'll say - and this is universal to my mental health struggles - it's easier now to deal with all such fears. Even though the object of the fear is larger (I'm even older! Whatever age cliff is in my mind is closer or has passed), it still doesn't bother me in such an aggressively agitating way.
Now, there's a separate argument as to whether that is a bad thing because I've just become numbed and complacent, but I think even diving into that introspection is part of the point. Applying to what you said, my advice would be that while you should "learn to accept it," that doesn't mean acting like the dread is misplaced or improper. Let yourself acknowledge that the fear has a legitimate place, explore why the fear is there, and then the "acceptance" involves seeing where it fits within your total psyche. (Metaphor because I can't help myself: being afraid of walking over a high rickety bridge makes sense. A fear of falling is natural and - frankly - logical. Rather than blindly "accepting" that you must cross the bridge, really look at how it's made, how many people have crossed it, how many of them are larger than you, etc., to understand why you can absolutely do it.)
Hope that helps a bit.
