Sleep training?

My baby is 14 weeks today. His sleep is a nightmare. He can fall asleep in his crib, but he wakes up after 30 minutes exactly and then I have to work to put him back to sleep again. When I try rocking him to get him drowsy, he screams and wiggles in my arms for 15-20 minutes before he will finally settle. Same thing for bedtime, but it’s a process of putting him back down every 30 minutes for sometimes up to 2 hours before it finally sticks and he does a 3-4 hour stretch. Can I just start letting him cry it out? He can’t connect sleep cycles and needs to learn to fall asleep independently. I tried last night and he cried an hour straight with no sign of slowing down, so I got nervous and picked him up. He’s on reflux medication, I’ve cut out dairy and soy, I know he’s not in pain. He just takes forever to get to sleep!