Is it normal that i don't like to be touched?

As a child/teenager I was never hugged or kissed by my parents, never told I love you. I received no affection at home. To top it all of I attended a highschool with very strict pda (public display of affection) rules. No type of pda was allowed, no hand holding with a boyfriend or even just a bestfriend, obviously no kissing/making out, but the most ridiculous was that you weren't allowed to greet or say goodbye to a friend/boyfriend. Just nothing. This has conditioned me to be put off by everything. I feel extremely awkward when anybody attempts to give me a hug. It no longer feels natural to me. Even a handshake feels weird. Any contact feels strange, almost foreign.

I have been with my boyfriend for about 2 years now and I still feel awkward holding hands, him putting his arm around me, or kissing me in public. I'm completely fine with it in private, when nobody is around but I feel too uncomfortable to do that in public.

When I say goodbye to him after he drops me off at home, I say bye, I don't hug or kiss him at all, I can't even say I love you. I really wish I could muster up the strength to do so.

I'm too used to being closed off and not allowing myself to be open and have intimate contact with anybody. It's affecting me internally (emotioanlly).

I yearn for him to put his arm around me and show that I am in fact his girlfriend to my family, his family, our friends, but I simply can't drop this strange veil of "this feels wrong/unnatural".

I wish I was brought up differently.

I wish I had learned how to be comfortable in my body.

Alas my question remains, is it normal that I don't like to be touched?

I don't feel normal :/ which is the worst part.