You sound a very sensible and caring person. You are also in a puzzling and worrying situation. Your saying that at first you were worried you were the cause or had done something wrong struck a chord with me.
I've been the one that has been depressed. At the start of my illness my wife thought exactly as you did, and only came to realize that was not the case as matters were explained to her by my doctor and my psychiatrist.
All the things your BF has done and talked about are very similar to me when depression has really taken hold, so I can say from my own experience yes it is normal to feel hemmed in and want space - though that is not the full story. While I felt I was a burden and that my family would be better off without me I was of course wrong.
My wife had a most difficult juggling act, to make sure I knew she was there for me -a constant in my life - whilst at the same time not crowding me when that made things worse and at other times being close. A just about impossible task. She has my undying admiration for her care, sensitivity and skill.
Like her I'm sure you may make mistakes or miscalculations, it really does not matter, care is what counts.
The most important two things are firstly you encourage him in the best way you can to seek medical help. If he is unresponsive to you, then see if there is some one else (friend, family, workmate) who can persuade him.
I kept getting worse until I have professional help, and that is neither that quick nor very short term.
The second thing is your own welfare. To keep optimistic, to have a sense of perspective, not to be ground down is very important. So what support do you have? Parents, siblings, friends? It makes a world of difference to be able to talk frankly to someone who cares. My wife had her mum. It would have been very different for my wife without her.
If you'd like more information on depression have a look at The Facts menu above. Also as Bethie suggest read posts right here in the Forum about others who have had difficult carer's roles too.
As I mentioned this is not a quick thing, and we would be very happy for you to keep on coming back and talking more