I remember what it was like wanting to know more about transgender issues right about the same time that the internet got going. Suddenly, I no longer needed to go to the library and search the card catalogues hoping to find some scrap of information about why I thought the things I did, and whether anyone else did too. The walls of The Closet are built out of shame and fear. You feel like you are all alone, and you dare not talk to anyone.
Then comes the day when your secret slips out. Is it really surprising that you are unable to tell the truth, the whole truth and nothing but the truth when you are being interrogated by someone you do not wish to frighten away? Chances are that you weren't even ready to tell the truth to yourself at that point. Getting it right on a moment's notice when the stakes are stratospherically high is too much to ask. Don't be hard on yourself if you made a mess of it. So did many of us in our turn.
The broken trust is another problem, and it's going to take a lot of work to undo the damage the you have done to the relationship. Ultimately, whether the two of you stay together at this point is going to be more her choice than yours. Wrap your head around that, quickly. You can't make her stay, and any attempt to try to do so is going to come off very badly indeed. You've already cheated and lied. Don't add "tried to control" to that list.
There are still things that you can do, and perhaps you can even affect the outcome. First of all, stop lying and cheating. You can't afford another screw up. Second, give her a pass for now on her toxic behaviors. It's an invasion of privacy to read someone else's emails/browser history, but you are hardly in a position to press that point. Third, get professional counseling. Your initial goal is coming up with a plan to survive whatever goes down. Yes, you can get some pointers on how to make things right with her and within yourself, but there's a good chance that things are going to get worse before they get better. Put together the safety net that will allow you to live long enough to have second chances. Don't lie to the therapist! Do some individual therapy before you start couples therapy. Let her know you are getting help, but don't expect her to give you a medal for it at this point. Be sorry. Be "I'd do anything to make it up to you" sort of sorry, but understand that there is nothing you you can do to make it up to her. You've been humbled. You're going to need to stay there for a long time.
I do wish you the very best. Transgender relationships can survive, but both parties need to be all in. Decide if you are. You owe that to her before you ask her to risk getting hurt even worse.
Posting here was brave. Stick around and let your self be supported.