If this is the single sticking point in your relationship and interactions then you do have quite a lot of control over its ability to cast a shadow over the pair of you.
If she brings up a health thing, let it go. Don't correct her. Then she won't feel the need to "correct" you back. It's possible that it's an area she is interested in and she isn't feeling all that different from you in the passive aggressive stakes. In the sense she might feel that you go out of your way to contradict her every time she opens her mouth about something medical. I'm not saying that is what you are doing, I'm saying it's what it might feel like to her if you look at it through her lens.
It's worth doing just to see if this is a single glitch the pair of you have, or if it is merely a visible symptom of something more difficult to resolve. She'll find something else to pick at you about if there is something of real note lurking under the surface of the relationship. If she doesn't... great. You can both enjoy your time together by avoiding the single trip wire into insta-irritation that exists.
I'm a TEFLer, (30 years) so I know what it is like to be exposed to a distinct lack of respect for your field and your work by people outside the field. Nobody in my extended family particularly respects what I do compared to the other professions and vocations that feature in the family. Including some who are "real"
teachers.
But that's OK, cos I only value informed respect. Informed respect comes from my peers, my students and my clients. I'm only going to get properly upset about a lack of respect for what I do for a living if those people stop giving it to me.
My extended family has other qualities, I love them and I can afford to let the occasional wince making comment to slide, in the name of smooth waters and a happy enough relationship with them. Nobody you are related to can, or will give you all that you want from them, all of the time. If it is just this one relatively small sticking point, you and your mum are probably in the top 25% of parental relationships on the planet. Even that group can have niggles and persistent minor annoyances causing fairly regular friction between them.
If it turns out it's less of a single sticking point, and more "the tip of a ruddy great iceberg"... then a heap of very different advice and support is going to be needed. Cos that's a different animal entirely.