How truthful can you be to your love one?? (relationship problem)?

I know you all may think I am insane. My boyfriend is really over protective of me and we are in a long distance relationship. Where he grew up the women aren’t allowed to show too much skin to men, like not hug or give handshakes, and you need to cover your hair. I grew in Canada where all this is something normal for us and we are used to this level of freedom we have. To be truthful and honest I have promised my boyfriend soon to be husband that I won’t wear swim suits, or hug guys and how I won’t show so much skin. I can show my hair but I can’t wear shorts or tops. I honestly wish I could be free whereas like this I feel I'm not but just because he matters to me a lot and I want him to know how much I love him and how I am being “truthful” to him. I don’t know honestly how much longer I can take this because deep down even though I love him with all my heart I just wish I could be like the other pretty girls who can get a tan, wear cute tops and look like I'm not dying from heat exhaustion. What can I really do? My friends think I'm insane basically, and my family doesn’t know about this. We are going to a road trip with my sisters tomorrow and they told me to bring my swim suit, I made an excuse and feel bad about it now. Keep in mind I can’t lie to him even though I lied to my sisters. I’m not really sure what I really want to do deep down. On top of all this I tell him everything and he thinks I am not telling him everything about what’s going on, when I do. I am tired of him not trusting me even though he says he does. Please don’t be rude. All I really did is some advice and sympathy. Thanks.