Why are you embarrassed, is it because you are doing embarrassing things?
Why should meeting a girl be something you don't want anyone to see, or someone seeing it is something you have to 'handle'?
The idea that game is something you do in public while somehow hiding from everyone at the same time doesn't make sense. If you are doing something you are not willing to have seen by the people you care about, you will feel like a hypocrite. If you are not willing to absorb all the tension of a bad outcome, no matter who is looking, it won't go well in the first place.
There's discretion, and then there's fear of judgement, they are different, one is just good calibration, the other is a false being.