I think it is lovely your baby likes to be close, you could try a sling as it makes it easier to carry your baby around. Your baby will probably be fine for a sitter and I don't think you need to 'break this habit' before going back to study. Children often behaviour differently for people who aren't there parents. You could try and get someone to sit for you for a couple of hours to see how it goes.

Make sure you choose your sitter carefully. No sitter should raise a hand to a child. If my sitter did this, well lets just say it would not ever happen again. YOur sitter could also carry your baby around in a sling if it makes him happy. This creates a close bonding. Some babies just need extra comfort and security, it is just the way they are, he will grow out of it eventually but is just not ready at the moment.

Your baby needs you, period.
Can you take on-line/alternative courses and put him in a hiking backpack while you study? Babies do not have a concept of what we call, manipulation. When he/she is older, he/she will. But for now, if holding him is what he wants...do it. It might seem like torture for you, for what seems like a long while. But this is a false illusion. This will pass. And it is worth it to comfort your baby. It is most important to meet his needs now, while you can. And remember, even if your very best friend is babysitting him...no-one will love your kid as much as you do.