What would your company do if a male and female worker had to make the road trip together? They certainly wouldn't put them up in the same hotel room.
When the physical changes start to happen on your body, you may be okay with sharing a room, but it is going to put your co-worker in a very uncomfortable position. That's not fair to him.
I think you should investigate what your company's policies are with respect to transgenger discrimination. If there is no policy in place, then your job could be at risk. But more and more companies have explicit policies in place to protect trans employees. In that case, contact HR soon.
Normally, your HRT status would be none of their business. But, given the shared accommodation situation, it is their business, in order to protect both you and your co-worker.