You need to sit your boyfriend down and talk to him. He has got to realise that you have the right to meet as many new people as you want, go out with anyone you like and live your own life. He needs to realise that he can be a part of it, no matter how many friends you have. Just because you are experiencing new things, meeting new people and having fun, it doesn't mean that you will forget about him.
It's unfair that he is giving you a hard time about it, he has no right to do that. It's great that he wants to spend time with you but you two have your own lives to live and you don't need to live in each other's pockets. When people do that, sometimes the relationship goes bad and they eventually break up. No matter how much you love him, you can't let him stand in the way of you having a life outside the relationship. If he can't quit his clingy ways and let you live the life you deserve then you need to seriously consider your relationship.
Go out for your friends birthday, don't let him stand in the way of you having a good time. Switch your phone off, leave it at home, and don't let him talk you out of going. Take a stand and tell him, show him that you need to have a life out of the relationship. If he can't accept that, maybe he isn't the right guy for you?