I have an invisible, well mostly invisible, disability as well and have unfortunately faced many of these challenges as well.
No one should be “forced” to use a wheelchair against their wishes and it doesn’t make the screening process any easier. When I have used a wheelchair TSA has been unwilling to provide any other assistance. They also have made me go through the regular line which is difficult with all the turns and people. I would also like to touch on the matter that a wheelchair isn’t always available even if you request one ahead of time.