When I first went I was 18, I was really nervous, but it went fine. It did feel a little awkward but it was helpful. Sometimes they have a little paperwork for you to fill out first- listing your concerns and describing how you see yourself- this kinda helped to warm me up to start talking about personal stuff. I've seen several throughout the years (mainly due to insurance changes) and I can say I got something beneficial from each of them. Once I saw a counselor and with her we never went too deep into anything- just touched on everyday stuff- but it helped to just give me perspective and have an ally. If there was something difficult I needed to talk about but wasn't ready quite yet, I told them so.
A good psychologist will totally understand and not take it personally if you don't click with him/her and need to try a different one. A good one will not judge you or be shocked by what you say. I imagine most of them have heard it all.
In my experience they have been kind and supportive. Should you decide to go I hope your experience will be the same.