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.