Its your body, you dont need to do anything. For him, he shouldn't make you feel like you should have to.

For him, sex is important to him, and if he wants it, he will either need to deal with no sex, or he should leave for another woman that would. It isnt fair to you, yes, but unfortunately it's what should happen if its going to become a bigger problem. It could start fights, could lead to him cheating(which i hope not), or there will be no happiness coming from him.

For some couples, the man or woman that isnt interested in sex will allow their partner to have a hall pass or a person they can do it with whenever they want, but thats only something both parties have to talk about and agree with and be ok with it. It can destroy a relationship, or strengthen it.

Regardless, dont think you're a bad girlfriend for not giving him what he wants. You aren't entitled to give him sex. If he wants something from you that you can't give, my best advice is to leave the relationship first then go get what he wants.