So am I! And, no, mentioning someone's age is not ageist in itself, any more than mentioning someone's race or sexual orientation is racist or homophobic.
Assumptions or assertions that associate age with a negative characteristic are ageist. Old people should avoid the shops at weekends because we're slow? Ageist. Boomers hoard all the money? Ageist. Ugly outfit looks like 'old lady clothes'? Ageist. The state pensions' a waste of money; old people's access to healthcare should be restricted; old people should be automatically offered assisted dying? Ageist!
Mentions of age-related health problems aren't ageist. They may well include discussion of shoes that are comfortable for time-worn feet - but younger people also have bunions, so it would be ageist to call comfy shoes 'old person' shoes.
Awkwardly, some negative associations with age are ubiquitous in a youth-obsessed society. I don't know if you've noticed that, now their biggest market has passed the age of 55, cosmetics companies are no longer advertising to 'fight' the signs of ageing. We don't like being told we've lost a battle, so now they're selling us our 'best selves' instead. An old face may not be as pretty as a young face, but it's ageist to call it ugly.
I have a particular loathing for the many threads complaining of parents having the downright cheek to spend their own money instead of giving it all to the OP but, unless they make a direct connection between age and greed or selfishness, it's hard to call them ageist. Most do, though, and pretty early on!
Mumsnet could and should do much better on this.