I don't know what brand he used, but one of my classmates covered his full sleeve with those UV sun protection / compression sleeve things. He wore white to match our scrub tops. I didn't, like, analyze the fabric up close to see if any color from the tattoos peeked through, but it served its purpose from a distance. Not that any of the nurses and probably most of the patients would have cared about him having tattoos, but...nursing school.
Another student with a half sleeve just wore a three quarter length shirt underneath her scrub top because she was prone to being cold anyway.
I understand its hard to accept your scars. Don't worry about what other people think, they're from a medical issue. For example, people with surgery or burn scars, some people can be uncomfortable with it but its their own issue, no one would tell someone with those scars to cover up, and if someone dared they would be shunned.
There are plenty of ways to cover your arms, for example arm sleeves like these. I also plan on becoming a doctor and my arm is all fucked up. If you wanna talk dm me. Stay safe.
arm sleeves and the classics, long sleeves, bracelets, etc