So in my county, the Netherlands, I can ask for a medical passport from my gp for when I travel. It listed all my medication and it can also list your capabilities or injuries. It is for when need to go to hospital so they have your information. I used to keep it in my wallet all the time incase I had an accident. But you can also use it prove your injuries when you have to make requests at the boarding desk for example.
I understand your point about a showing disability. When I was on crutches everyone would get up when I got on public transport. Butt you cant expect people to know you have an injury if its invisible. After I got off them but still couldn’t stand for long periods of time I would just ask people to get up. Don’t be shy or embarrassed. I’ve never seen people make a fuss. You just say excuse me I have a multiple back injuries may I please sit here as it is handicap seating. Or even a “normal” seat. I’ve never seen anyone say can you please prove your injuries. Because if you don’t have an injury you wouldn’t be asking. I hope you’ll stand up, or I guess sit down (hehe), for yourself more. Don’t hurt yourself because you are afraid what people might say.