You know what, you start to feel old at any age. I know it isn't the most helpful advice to say don't worry about it, but you really shouldn't. Heck, I think you'll learn to stop. Oh, that feeling will always come back from time to time, but then you'll also have feelings were you feel young and energetic. I think anyway. It wouldn't be fair to generalize. Just basing things on my human condition.
And there are advantages to feeling old depending on how you feel old. If you feel old in the sense that you feel like you can be someone's mentor or someone who seems dependable in a certain way, and that's a good feeling.
In some ways, I feel old, but in others, I feel like someone who is still a child acting like an adult and thinking that I am the exception. But I don't think I am (especially since in recent years there seems to be a lot of pop culture that explores that concept).
I'll admit this is more stream of consciousness on my thoughts of aging, but here's my advice: as I said, from time to time you're going to get hung up on it, probably. And I know you've been through enough so a The Room-style "don't worry about it" isn't a sufficient answer sometimes. But I think you are going to find yourself feeling, if not "young", then perhaps vibrant, re-invigorate or energetic and know that you will experience things that will make you question this whole "how old do I feel".
So I guess, I am saying "don't get hung up on it". At least in terms of expectations of what age and what you might be expected to feel.
Hmm... Does that even help. All you really said is "I feel kind of old recently". I hope some of my ramblings produced something to take in.