am I a bad girlfriend?

Me (28F) and my boyfriend (30M) have been officially dating for two months, we're co-workers so we met last year and he immediately fell in love with me. Long story short: he started showing his love in every possible way (sometimes it was way too much!) he bought me so many nice things even for my birthday and we weren't even a couple, we were just talking and i wasn't sure about my feelings for him. He's always been so caring, sweet, our conversation were incredibly full of so many beautiful things and i always felt at ease with him. There's 1 big big problem...while he's so passionate, he wants to see me everyday and spend every second of his life with me, there's me: an introvert, suffering from depression and an ed (i've been in therapy for years, i'm okay but there's a lot of work to do..) i love my time alone, i'm an only child and very used to do everything alone. I feel incredibly guilty when I'm with him and suddenly my social battery say "okay it's enough" i feel tired, i want my space and I feel sad because I love him and i don't wanna hurt his feelings. He knows everything about me, and he "accepted" the way I am, but i know that it's not easy for him. When I'm with him I feel fine and I'm happy, but I feel split right down the middle. I enjoy my time with him but I also love spending time with my self and it's my kind of therapy. I don't know why it's so difficult to me spending time with people, that includes my friend and family of course. I love them deeply, but I just can't sometimes. I feel so bad, maybe I don't deserve love, maybe I'm not right for this world...