Hi Nordic, I'm glad you posted
I'm an introvert too. I know exactly what you mean when you say people drain your batteries. It takes a lot of effort for me to spend extended amounts of time around other people, and if I don't get some alone time every day I start to get irritable, jumpy, and very, very tired. Some of us just aren't social butterflies.
I think that the reason your doctor presses the issue of companionship is because humans are, by nature, social animals. We just happen to have evolved that way. I think what your doctor is more concerned about is that you have someone you feel you can open up to about your problems. Depression is a torturous illness to have, and sometimes it can help to talk about how we're feeling with people who care about us. I don't think he wants you to start going to every party and changing your lifestyle in dramatic ways; he's probably just concerned that you don't have anyone to talk to, to help you release some of the things you might have on your mind. It's comforting and therapeutic to talk things out. Depression tends to isolate us to the point where we spend most of or all of our time with our own thoughts, which can become very painful if not dangerous. The companionship of others can help us deal with those thoughts, or maybe help us forget them for a little while.
If there's no one in your life you feel you can talk to about this, what about a therapist? If you don't have one, therapists are fantastic because you don't have to keep up any kind of facade with them. You don't have to work on your relationship with them. You don't have to pretend you're fine when you're not, and you don't have to try to impress them. They don't drain your energy in the same sense as being with other people because you're not there to socialize, you're there to work on getting well.
I'm very glad you posted and I hope you keep us updated on how you're doing.