Hey, I know how you feel, I am like this all the time even if it would be a fellow Christian who catches me praying… or with whom I would pray before a meal. I agree that we should not be ashamed to pray… If we feel shame, that, I believe, is a “disordered” emotion. We can’t control our emotions directly, but we can control our actions. Honestly when it comes to praying in private and people “catching you,” I have made many mistakes. The more often I try to pretend I am doing something else, the harder it becomes to just pray and not care what people think. We just have to make a deliberate choice to pray even if people will see us, even if it makes our skin crawl and we feel quite unpleasant. I used to be terrified of making the sign of the cross at unusual times (still am sometimes), but now I can do it pretty easily (at least in the car). You just have to keep doing these things even if it scares you, and eventually you don’t care anymore what people think. of course, it is easier said than done.
Also, regarding prayer before meals. If the people aren’t Christian, or religious, it might be weird to pray before meals… but if they too are in the habit of praying before meals, or you think they would not be adverse to it, then you might ask, “Do you mind if we pray?” and yes the sweat may run down your face and whatever (it does for me and I am petrified) but it is truly a matter of forcing yourself to… but praying before meals because you feel like you MUST and not because you want to, and are focused on the meaning of it… try to refocus and think about WHY you would pray before meals… is it because you HAVE to, or because you want to bring the focus to God when perhaps with friends you become distracted, etc.