As everyone else has advised, carefully work through this with your therapist. Honesty is always the preferred path to follow here as well as in most all things in life but disclosure is a process.
Disclosure to wife or SO is often misunderstood as a simple process, akin to simply mounting the courage to sit down with her and begin with "Uh, honey, I've got something I need to tell you..." This needs to be understood as a far more nuanced process, on which you will will spend substantial time and effort with your therapist.
If the burden of secrecy is weighing on you to the point of depression and disabling anxiety, you will need to confront the need to disclose in some manner as one of the initial goals. What might be useful at this time in the process is to begin gently probing, testing your wife's positions and deeper feelings in an attempt to estimate her responses. Also, be forthright about seeing a therapist. At this initial stage, you may want to tell her (truthfully) that it is because of your anxiety and depression, an attempt to improve your situation, be a better happier healthier spouse. You do not need initially to disclose you are seeing the therapist for concerns over gender--that will come later.
Many, if not nearly all of us have struggled over the secrecy issue. First, realize that you are not hiding a grim fact such as the undisclosed fact of having murdered or raped. You've done nothing inherently wrong being who and what you are despite the guilt you feel over it. Emerge from the sense of guilt and move on. Here is where you need your therapist (in a big way). Conversely, I'd advise you not to swing to the opposite extreme in response to this realization to the position of playing the victim. Society is what it is. Acceptance is less of an issue than often anticipated before coming out. Try to emerge from guilt into a mindset of actively managing and living your life, including this previously hidden and suppressed aspect of it.
Back to the honesty issue and disclosure to you wife. I had to work through a deeply disturbing sense the failure to be entirely forthright and honest with my wife being a overt lie. I, again like most of us here, have known there was something wrong since childhood. Read the Anne Vitale piece on her website,
http://www.avitale.com/developmentalreview.htm which might offer some insight into the problem at different stages of life. In any case, be gentle with yourself. I've come to realize, that I did not even understand the nature of my own problem until well into mid life, nearly the exact description A.V. describes as the "group 3" individuals, illustrated by the example of her patient, John, in the essay. Realize you've tried to find a practical path through life, done the best you could, now find this effort failing and need help. Try not to judge yourself to harshly--realize you've made utilitarian compromises to allow life to go on, in the largest extent, in in attempt to protect your wife from something that society finds difficult to accept--at high cost to you and your mental health. Now is the time to work toward a solution that will allow both of you to emerge from this compromised situation to a healthier one.
Therapy is a wonderful thing when done well. The spectrum of solutions to gender dysphoria and management of conflict between natal sex and ultimate gender identity is vast and very personal. If you feel you are getting to a dead end with your current therapist, don't despair, there are surely others who may be better positioned to help you.
