Maybe because of being newbie in physical casinos that's why you have a shyness in gambling. I am also shy especially if there are a lot of people watching you when you play especially when they look at you because you are new to that place. I think it is normal with casinos but eventually your shyness will gone after all.
Sometime i was feel shyness, but don't be shy, it shows only that you can afford to play in that casinos. What you feel is similar to others who is watching you when you play, so just ignored that kinds of feelings. Don't get affected to those people are watching you. Think of that they don't care the important is you want to play just for fun and to earn.
Shyness might come when you are doing something unusual and people are noticing you. Else if its legal in your country and you are of a legal age then you can go and play and without being getting any embarrassed should play it. For a newbie it can occur to an extent since very new to the feeling and seeing people gambling their with huge money might feel awkward who has come with a little spare money to play with.