Is there any way for natural age to be raised unnaturally? I ask because some of my characters seem to be older than they should be.

Yes. The most prominent way is from the attacks of certain kinds of the creatures in the Mire of the Damned (I think one of the ghost variants do it). If you open your character screen and check your age, unnatural aging shows with a green number (as if it had been "buffed").

Drink a Rejuvenation Potion to remove unnatural aging.

Creatures who cause unnatural aging: Evil Spirit, Harpy Witch.
When characters become magically aged - they scream and lightning goes all over their portrait.
Keep those in mind if you want to avoid magical aging by reloading when it hits you.

Rejuvenation Potion permanently drops your stats if you use it, so only use fountain in "Hermit's Isle" world zone if you want to remove unnatural aging without penalties. That zone is a very high-end zone, so... keep this in mind.

I know about unnatural aging. What I'm saying is that I have my natural age higher than it should be, before the unnatural aging is applied

Unnatural aging is shown in green number.

Can you give the screenshot, showing the age? If you use in-game calendar, what year it says it is for you now?

Screenshot is here: https://imgur.com/zYoDyiF and the year is 1165

Looks like you got hit by one of the aging monsters, making that character 31 years old.

26 years old as the normal age seems fine to me.

IIRC, a character can start as old as 26 right from the beginning.

Oh. I didn't know your starting age was random.

Extreme Energy White +20 statistics temporarily Orange + Yellow
Rejuvenation Black Removes magical aging, -1 statistics permanently Green + Extreme Energy