I'm in a long distance relationship so, although I see my boyfriend a considerably more often than you do yours (longest time apart has been 6 weeks), I completely recognise the feelings you describe. Lethargy, lack of motivation, sleeping difficulties, floods of tears - I've been there, done that, for over three years.
It sounds to me, like what you need to do is talk to your boyfriend. The fact that he says you need to sort yourself out either shows a lack of understanding on his part or - worse - suggests that he doesn't care about you enough to help. Surely he understands that he is a huge part of the problem? The fact that he is surviving happily and comfortably without you is only going to make you feel more separated from him and more lonely.
How often do you have contact with each other? Do you text every day? Skype once a week? What are your communication patters like? Is it regular? Is it him initiating the contact or is it always you?
My boyfriend and I used to send one email per day and skype once a week and I thought that was enough, but then I realised that I was really miserable and missed him constantly. These days, we skype almost every night and the fact that I get to see his face, listen to his voice, hear him laugh and tease me, makes me feel so much closer to him and I'm much happier now.
It works for me and maybe it'll work for you too, but the real problem seems to me to be the disconnect between your feelings and your boyfriend's understanding of them. If he loves you like you love him, then he should want to support you and help you feel better, not force you to deal with it on your own. The best advice I can really give is just to talk to him!