Melatonin makes me sleepy the entire next day

Hello r/sleep!

I started taking vyvanse (which is a stimulant) for my adhd a month and a half ago. It wreaked absolute havoc on my sleep but I pushed through for a few weeks hoping the issue will resolve itself. It makes my heart beat faster so just lying down is really uncomfortable, and my brain keeps going so I usually just get up and do some work.

My doctor gave me 3g of melatonin to help me sleep. I've been taking them around 3AM to wake up for work at 10AM. It does help me fall asleep and I wake up feeling well rested but I noticed I feel so sleepy the entire next day and have to take multiple naps until I feel normal at around 6pm. I stopped taking it which sucks because I sleep even less but at least I'm still energized when I wake up and usually crash around 3 or 4PM so I take a 2 hour nap then.

Is this normal? How long is melatonin supposed to stay in the body? Should I cut my pills in half so they don't affect me as much? Is there a minimum amount of sleep I should have so melatonin is out of my body by wake up time?