Is it normal to be so nervous about my first therapist appointment? Can I really tell him how I feel?

I've had lots of therapy and I'm not ashamed to say it. Everyone needs help now and then. The people who don't get it suffer.
If your apprehensive go slowly. Only speak of the problems in increments until you get a "good feel" for the person and trust your instincts.
I always find out where they graduated from. The better the school the better the therapist. You can check the person out online by typing in the person's name.
Hope that helps you.

Well, this may sound kinda hokey. But trust in the process. And don't worry so much about crying. You'll stop, eventually, when the time is right. Feelings can be powerful, but none last forever. Trust your instincts with your counselor.

Wanted to add- I am a confirmed, active, worshiping, praying Christian, and I would advise you not to narrow your list by religious criteria.
My personal reliance on my Faith does not intermingle too closely with my depressive and anxiety symptoms, and my belief system is firm.
Therefore, I want to be talking to someone who will help me consider my behaviors in a way that will be novel to me, and I will trust myself to be smart and aware through my therapy to contrast feelings that may seem out of kilter with my Faith, and learn from that kind of comparison how to reconcile the pain and frustration of caregiving with the joy of helping a less than cooperative LO.
My present therapist was raised in my personal Faith, and may or may not be active in it now, and we have NEVER had any conflict in belief.
If I sensed any potential conflict, I’d be looking for someone else.
TRULY SORRY that you wound up with the wrong counselor in your first attempt. Please give it another try.

My 86 yr old mom had a therapist as she was neglected and abused. One day mom was sleeping and she asked mom if ok to talk to me? She was very helpful she told me she was more worried about me than mom