How do I handle this?

I have been with the same trainer for a number of years. Over the last couple of years I have had the opportunity to groom for another trainer at shows. One of the tasks that I perform is braiding. I’m not the greatest in the world, but if I compare to the other jobs, I see at these I am at least as good as they are. My current trainer has made it clear that she is not a fan of me doing this. She has made comments about the other trainer that I work for that have reflected her opinion of that trainers abilities. Lately when I’ve been at the barn, my trainer has made remarks to other people That seem like Compliments, but I know they are backhanded slaps. One time she told another client that I was picky, and she didn’t mean it in a good way.. I responded that yes indeed I was picky but I was picky about the work that I did for other people not about what people did for me. Another time one of her clients was asking her about some struggles She was having with braiding her horse. my trainer responded “Oh, ask (Insert my name here), she’s a professional”. There were many people standing around at the time and they all knew she was taking a dig at me and disguising it as a compliment. I was embarrassed, and I didn’t want people to think that I thought I was something that I am not, so I said “ No, I’m not a professional. I do have one client and she does pay me, but I am by no means a professional.”

How do you think I should address this or am I being too sensitive?