I don’t know your whole story, so I don’t know your relationship with the doctors (new patient?)
From what I hear a lot of doctors don’t prescribe self administered injections if they barely know the patient.
On the other hand- maybe that doc has no experience prescribing that type of treatment…
As for the Testim and your concern for your daughter- just wash your hands really well after applying it, and put on a shirt. After a few hours, it’s my understanding that it should be dry enough and absorbed enough that it shouldn’t effect other people. However, I do see your concern. I have a boy, and was concerned when I was put on Testim.
FWIW, there are very low instances of secondary exposure reported. Just do the best you can to keep it away from your daughter while it’s wet on your shoulders, etc.
Also- it may be worth it to call around to compounding pharmacies and ask them if they know of any good doctors for HRT or TRT. Sometimes the best doctors for HRT are not endocrinologists, but rather a family doctor with a special interest. Good luck.