I understand, I had the same with my industrial before deciding that I'd rather be without it than pushing through the pain after every bjj class.

I'm guessing it's a standard bar? See if you can find a thinner one. Otherwise, if your trainer meant something like this: https://www.amazon.com/Training-Protector-Martial-Kickboxing-defense/dp/B00BA1Y554 (just an example from a quick Google search)

It could be worth the "hassle"