Why does she treat me like this?

My girlfriend always acts as if she is doing me a favour by being with me, but this happens only in public. In private, she is loving and kind which is why I am always confused about where things stand. When I ask about this, she says she has to pretend because she doesn’t want anyone to think she is with me for the wrong reasons. I understand that this may be because I come from a rich family, but it is still hurtful. I don’t doubt her love, but I worry about how my friends and family will interpret her behaviour and don’t know how to get her to just act more normal. Will this just get easier with time?
There are all kinds of reasons why insecurity can make someone behave in a way that is unnatural as well as hurtful. Your girlfriend may have valid reasons for pretending to be haughty, but the priority in any relationship must be how the other person feels rather than how family or friends may interpret anything. This is a question of misplaced priorities and may require you to reiterate why her behaviour may cause more harm than good. It is also important to try and understand he perspective and get her to open up about what she’s struggling with, because it will help you make her feel more comfortable. If she feels as if being with you is a safe space where she can be herself, there will be no need for putting on an act any longer.

Our relationship is falling apart since my boyfriend moved away, and I don’t know if it is even worth trying anymore. Should I assume the distance will prevent us from making it happen?
Distance can be a factor but only when two people have decided that they aren’t interested in making something work. It’s difficult, but not impossible. Have either of you spoken about whether this is a relationship worth saving? Start with that conversation and see what he says.