OP, I can relate to your girlfriend a lot, actually. I do have friends but I'm an introvert and find it so much more comfortable to be on my own, and I do have hobbies (solitary ones) so I'm perfectly capable of whiling away time myself, but my relationship is a huge part of my life and if I feel that my boyfriend isn't very keen on spending time with me I'd worry that something is going wrong with our relationship. To be honest I'd consider it a pretty bad sign if my boyfriend prioritises his friends over me.
It sounds like that your girlfriend might be suffering from low self esteem (like me), which leads her to think that other people including your friends dislike her, and feels that she's not worthy of your attention when you'd rather spend time apart. I'd say the best thing you can do is to reassure her that she means a lot to you, and that when you choose to do things without her it's because you need some space to yourself, and not because she's low down on your priorities. Do you still keep in touch with her when you're not with each other? You can send her an occasional text when you're hanging out with your friends to show that she's still on your mind.
If you've already brought up seeing a doctor for depression and she refuses, there's no point in bringing it up again. She'll seek help when she feels like it, but being told over and over that you need help can make someone feel like they're a broken thing that needs fixing.