As an extremely closeted trans woman I felt similar anxiety about sharing my secret with anybody. Coming out to my counsellor was super hard but I eventually managed it right at the end of the first session (after we'd already gone over time by 30 minutes).

A counsellor/therapist is the absolute best person to come out to first because they're absolutely not going to betray your confidence, and they have your best interests at heart. Personally I recommend finding a counsellor who practices Person Centered Therapy based on Carl Rogers' work. The core values of PCT are Congruence, Empathy and Unconditional Positive Regard. Congruence means the counsellor must bring their real selves into the counselling environment; empathy means they must try to see your issue from inside your perspective (i.e. how you yourself see it), and unconditional positive regard means they must not judge you but hold you in high esteem as a fellow human being going through real and important struggles.

It's those three core values which gave me just enough confidence to tell my counsellor the truth of why I had come, and I'm really glad I did. 2 years later it's a slow and painful road but opening up to my counsellor eventually gave me the courage to tell a few other very close friends and start to see myself in new lights.

I'm sorry you're going through what you are. It sucks and even as someone with a four year theology degree under my belt I can't pretend to understand why God lets us go through these utterly shit experiences. But, even though it took me a while, I can at least believe that God loves me and wants the best for me - even if I have no idea what that looks like this side of eternity.