If I’m not too late I’d say certainly Yes. As you are both ‘in the trade’ I’d suggest booking the appointment then having THE conversation with your wife as soon as possible. She may well think something is wrong already as she’s tracking your phone. My ex-partner is a nurse (formerly QMC Nottingham now in Australia) and humans are humans so they do talk shop, if she finds out like that you’ll do well to get out alive.
I took the afternoon off cleaned the house, did the chores, ordered her favourite meal from the restaurant and bribed the kids to give us the evening.
I needn’t have bothered, I practiced my pitch (I strongly suggest you do this too) and just started when she cut in ‘I already know, you’re transgender aren’t you?’ I was utterly pole-axed. So much for keeping up an act. I am very fortunate but got bonus points for the care I’d taken to tell her.
One thing is that this isn’t anybody’s fault – you have a previously unrecognised condition and are seeking a professional opinion to move forward. However you may find that you lose everybody and nearly everything you currently have, if that doesn’t deter you then it’s a real issue that needs attention or you’ll be heading into dark and horrible spaces. I’ve been there and it nearly killed me, don’t do the same.
I’m still on very good terms with her mother and apparently concerns had been raised some months before, my ex- had gone through the ‘he’s having an affair’, ‘he’s gay’, ‘he’s got something horrible and/or terminal’ and ‘he’s got a terrible secret’ routines before getting to the TG conclusion. Once we accepted that it was nobody’s fault acceptance was easier and here I am now.
Good luck and I hope you get a good outcome too.