This is quite a common thing so don't worry that there's something wrong with you. It's also quite common for a guy to NOT want his girl to wear revealing clothes.
It is good that your girl is OK with what you're asking her to do. I find that shared interests and more importantly values are really important in a relationship.
Guys do like to show off their girlfriend to other people - it's all part of the power play of being a man. I found a beta guy write this on Quora: "I think he wants to showcase you as a trophy and to show off to his friends and to the world. This is totally weird and maybe you should express your disagreement right away instead of compromising."
There is absolutely nothing weird with a man wanting power and status!
For a girl that can be flattering even though feminism tends to denounce this sort of thing.
I guess the sensible approach would be somewhere in between.
Look for signs that you're becoming controlling, as that can lead to huge life complications. When we get stressed we tend to project our insecurities onto other people, which is another thing to be aware of.
Even though you're in a great relationship with a girl you adore, just remember to keep other parts of your life going. Visit the gym, maintain your hobbies and go out with your male friends once in a while.