listen to your heart. if it doesn't feel right to let him cry, then don't. mothers know best. your ped's suggestion is easy for him to say cos he's not the mom listening to her baby crying. & it depends what age your ped is. i think the older generation believe we shouldn't "spoil" our babies by carrying them. i used to believe in that and struggled for so long cos my daughter would cry so loud & long if we didn't rock her to sleep. she'd vomit & make a big deal and it drove me crazy. it was because i wanted her to learn to "fall asleep by herself". once i accepted that she's just a baby & it won't be long before she didn't need us to carry her, it was OK for me emotionally.
we did carry her to sleep until she was around 2. one day i just told her she's too heavy to be carried & i sat next to her & put my hand on her to let her feel secure. and she was OK with it.
she just turned 3, and we only carry her at night when she's not well. but once she's drowsy, she wants to go bed by herself.
i think babies are only small for so long. by he's 3, you can't carry him or he won't want you to carry him. so it's only gonna be 2 more years down the road (i know it sounds like a long time to you). look at it this way, it's just 2 or 3 years in his, what, 70, 80 years of life? carry him as much as you want to now, since he's still so small & light. when he's 10, you'll look back & be glad you carried him as much as you could. cos he won't let you carry him after he's 10 even if you beg him!!
good luck with motherhood!