20 week old still waking up 3 or 4 times a night?

It's important your baby learn to soothe themselves to sleep early on. I agree with your doctor. You would also wanna lay off the mid day naps that extend beyond an hour and stop feeding at night. Right before bed and that's it. Your programming him to wake up to eat in the middle of the night. So close the kitchen! lol, I know it sucks having to listen to your baby cry when you have the power to stop it but you have to think long term here. It's gonna be better in the long term.