Transgender Support Group
This community is here to support and help the large population of transgender people. If you or anyone you know identify as transgender, this is the place to share your feelings and experiences and speak with others who are going through similar things in their lives.

The second thing that might help is that you don't have to tell them what he appointments are for or you can tell them something generic. You list here you have depression, tell them you are going to therapy for depression. Depending on your insurance and what it covers, its possible that at least the therapy would be covered fully. If that is the case then it will just be getting to the appointments.
In the long run this journey we will call it, is not about changing the body nor the mind so much as becoming comfortable with ourselves. So you need to find what will make you happy and go with it, if that means hiding in plain sight then do so, if it means hiding then that is fine too. You are on a path with the SSDI that will take time, so will the trans thing and neither is really completely dependent on the other. That said, it will cause stress having them combined and coordination is a pain, but you do not have a stamp on your head or a big sign over it. Most people will ignore minor anomalies so you can get by with subtle changes for your own comfort in the short term at least.