I think everyone has given really good advice so far. I've never had a jealous partner, and my husband is not the jealous type either, we have complete trust. It wouldn't enter either of our heads to cheat on each other. But that's not really important anyway. A relationship is a 2 way street, there should be give and take - on both ends. 😉
I have had friends in the past and just recently, that have had 'jealous' boyfriends, and all of their relationships ended badly. Of those, 99% turned into violent relationships. From what I've seen of those relationships, the possessive, jealous, controlling types usually are violent, or eventually become violent because to them, you are just a possession, you should have no free will of your own, and I'm not referring just to men either, it also goes for some women too!
If he truly loves you, he will trust you - and if you love him, you will trust him too. A relationship without trust really isn't a relationship because it's never going to be healthy.
My cousin's ex-partner was diabetic, so I understand about the mood swings, but usually that was when he wasn't managing his diabetes as he should be.
If your boyfriend is having mood swings & sleeping alot because of his diabetes, maybe he's not looking after himself as he should be & perhaps not managing his diabetes properly? I know my cousin's ex-partner's neglect of his diabetes nearly put him in a coma once... Funnily enough, since they split up, he has never been healthier 'lol'