When you go to a doctor and are too embarrassed to say straight out what the problem is, the doctor isn't going "oh my goodness how awkward." They're going "SPIT IT OUT ALREADY. Did you jam something up your butt? Do you get an erection when someone hops on one foot in front of you? Tell me what the friggin problem is so we can deal with it." The only person at all concerned with it being embarrassing is you. They're just sick of dealing with people who are too embarrassed to get proper medical attention.
Gynecologists have to check for cancer in women by sticking a finger in the butt AND the ladyparts at the same time and feeling the wall between them for bumps. And that's just a standard preventative procedure like having your blood pressure checked to them. Man doctors have to fiddle around with the man parts to check for problems, too. If you go to the doctor and tell them your butt is mysteriously itchy, they just pull your pants down and poke around until they find the cause. Believe me, I know. If you can't pee, they grab your parts and shove a tube in there. It's all just... part of the job. Seriously, there is literally nothing you can tell a doctor that will make them feel awkward or embarrassed, and they're really just annoyed with you for stalling because they have other patients to see with stuff stuck up their butts. The most uncomfortable part for them is the part where they have to wait for you to tell them what's up. Busy busy busy.