I felt kind of like a science experiment to everybody involved in my follow-up appointment for bottom surgery. The appointment wasn't with the surgeon or anybody professionally related to him; it was with a fairly 'small town' doc and tests were done at the local Catholic hospital. Awwkwardness. Everybody did remain acceptably professional, I think, it was just that it was obvious that none involved were familiar with or had seen 'that kind' of surgery before.
For the two 'down there' exams that I had while on T (after growth), I lucked out with a completely awesome trans-friendly P.A. who actually has some knowledge on the subject. She was a completely unexpected, amazing person to find. I felt like she at least had a basic understanding of what she was dealing with and how to handle it; I never felt like a freak show, at all.
I wouldn't shell out money for tests due to doctors freaking out over size. However, it may be in your best interest to tell them your history with taking testosterone. The growth that T can give is probably out of the norm for a 'female-bodied' person and, if you're seeing a doctor for problems with your junk, they might think that the two are related; I can understand why they might want to order blood or chromosome tests.
As for the small-town doctor privacy concerns--can you make an appointment for an out-of-town doctor, maybe an hour or so away?
And finally: I'm certain there are medical professionals who aren't as professional as they claim to be. "They've seen it all!" only applies when they've actually seen it. The chances of a small-town doctor having prior experience with a trans individual or someone with a trans-related history? Not that much, I'd wager.