T.R.
Believe it or not, there is such a thing as "sleep hygiene". This is the process of setting yourself up for sleep - making sure to eliminate electronic devices for a period before bedtime, having a calming routine in the late evening, keeping a regular time to go to bed, avoiding stimulants like caffeine, limiting naps during the day, etc.
Since you need to wake up during the night for feeding, I would NOT recommend any type of medication to help you fall asleep - you need to be able to rouse from sleep to tend to your little one. If you are breastfeeding, you should also avoid supplements like melatonin.
Here are a couple of links that talk about setting up a sleep hygiene schedule that should help you to get to sleep. It may take a week or so of adjusting & sticking to a routine before you notice the benefits. Because you don't have difficulties falling back to sleep after feeding, I strongly suspect the problem is making sure that you are properly tired before attempting to fall asleep. That may require adjusting naps & exercise to find the right balance of energy expenditure, so that you aren't exhausted, but you are ready for sleep when 10 o'clock (or whenever) rolls around.
Hope this helps, sweet dreams to you! T. :)
https://www.sleepassociation.org/patients-general-public/...
http://healthysleep.med.harvard.edu/healthy/getting/overc...