So glad you had a good time - knew you would because he sounds nice, keen and you get on well. All the doubting is your anxiety.
Like others have said, I wouldn't text, phone or push 'the talk' unless it crops up naturally.
There's no issue with him or you or the relationship - sounds like it's ticking along just lovely. The issue is that darned anxiety.
You've obviously decided to distract yourself and not let it ruin a lovely night which I think is exactly the right thing to do.
Anxiety is a bugger but you're tackling it. Good on you. I think you've got a better handle on it than you realise.
Sure, you flip flop on here at times with all the differing advice and your inner doubts - "I don't know what to do" - (perfectly understandable) but one thing I've noticed is you always end up making a sensible decision, like this morning, for example - you know it's the anxiety, taking a tablet and watching a film with DS.
You sound lovely. Switched on, level headed and strong. But because you have anxiety right now I think you doubt all that.
Give yourself credit. What I'm reading shows you have a good gut instinct keeping you on track and great self-awareness. An excellent quality imo.
Keep doing what you're doing - realise it's the anxiety, take the tablet, take a deep breath, distract yourself and deal with anxiety. I think you said you're starting counselling? Brilliant. Basically, all the things you're already doing. See? You do have a handle on it. 
TL;DR 
Just enjoy it. It's not you or him, it's the anxiety. You're tackling that. You sound pretty fab so in all likelihood will kick the anxiety in the windpipe or at least sit on the f.ecker long enough to mute it when needs be. Enjoy your DS film time! 