not getting much done help plz

Hi guys, I'm a ftm of a 5 months old. It has been very stressful dealing with my son as he's constantly fussy and needs to be looked after.
I have a big exam in June which I've been trying to study for but I'm not getting much done because I have no time. My son doesn't fall asleep till about 10pm- I take him to bed at 8. By that time I'm tired myself and get ready to go to sleep. He wakes up for two hours during the night thinking it's play time and then in the morning I'm either feeding him, or putting him down for a nap. He doesn't stay in his swing for more than 15 mins without getting fussy. I spend 45 mins trying to put him to nap for him to sleep for 30 mins.
I don't have anyone to help me and there is no way to postpone my exam. 
My question is: hoW do you find time to get things done??