I used to work in mental health field in my region and it has required adjustments to my treatment. My therapist is from another region of my country, and my appointments are online. But I used to work with my pdoc in professional capacity a few years back. Initially, it helped me to contact her because I knew she was not scary and we got along. Also, since I'm sick enough to need social services which was my own vocation, I've had to work with several people I knew professionally. My current case manager is someone who used to storm in my office and demand money for her clients' services (I quite like it now :D )
Did you discuss your previous acquitance with your T before you began? I've done it in every case when I know the person beforehand. Each must think through if they feel comfortable doing it. And then it's a must to change the relationship. I don't chat about her dog with my pdoc anymore. Or refer to her daughters in any manner, even though I know her family. When I'm the patient, it's strictly about me. It's one-sided relationship, and both parties need to stick to it.
Also, there are safeguards in place. When I'm sick enough to need inpatient care, there is a note in my file stating I'm never going to be sent in local hospital because I worked there. I go to another hospital instead. It ensures that I'll get to be a patient like everyone else, and also protects my privacy. It's a common psych ward practice here, healthcare workers are never treated in their own region.
I find it very unprofessional that your T accuses you of asking too much. Your T should have their own support systems so they can do their job. I don't know how it's in USA, but here a therapist must go through her own therapy before graduation and also have regular sessions with seasoned professional to get professional guidance and a chance to care for their own mental health. I find it integral to be able to trust my T can take whatever I bring to session. Otherwise there would be no healing, because I could not speak honestly. I need to pick and mix my experiences with every other person to regulate what I can say to avoid negative/upset reaction, and in two years I've started to trust she can take honesty. It happened quicker with my pdoc because I knew her before, and she is perhaps twenty years older than me.