A lot of people walk in to shops with different kinds of baggage relating to their body. Some people are conscious about scars, some don’t want a little fat showing when getting tattooed, some are self-conscious about their skin color and others are feel that they’re too skinny, among other things. You may find that going to an artist to have an area on your body that you feel vulnerable about worked on may boost your self-confidence. It may, and probably will, change your perspective on that body part.
Artists have seen an array of people with a variety of vulnerabilities and issues. Many have “seen it all”, as they saying goes.
I have personally had scars tattooed over, on my chest. They are from surgeries due to skin cancer, and I had always felt self-conscious of them since I got them, For me, it was important that my scars were camouflaged within the tattoo. My artist did just that, and now it’s a part of my body that I absolutely LOVE showing off.
What’s the worst that can happen from going and chatting with someone? You may end up with a piece that you can’t wait to show off, or you may decide to not go through with it. At the very least, you can express your fears and desires to someone, which could hopefully lead to some healing.
They probably have something they put up for tattooing "exposed areas" that would require taking off an uncomfortable amount of clothing - most often drapes or a movable screen.
A whole lot of the tattoo community is SUPER non-judgmental. I don't think you're going to run into an actual problem. You're in your head about it. The tattoo is going to be cool, and you're going to have a good time getting it and maybe some day you'll enjoy taking your shirt off!