Yep, you will need to offer the breasts lots if you want your supply to increase. Every 3 hours is not enough. Your doctor is not a breastfeeding specialist. Many newborns will nurse 18 times a day!
My suggestion: Offer both sides every 1 hour while your baby is awake. At night, every 3 hours would be good. You may find your baby will be willing to feed, even when asleep. If you can't do every 3 hoursat night, allowing one 5-hour stretch of sleep at night should be OK. Sharing a bed with your baby can make nighttime feedings easier. We can give you info on safer bedsharing if you need it.