ftm needing some reassurance

So my son's Ped. told me I needed to start letting him cry it out at night time some.. he's been waking every two hours (we had some nursing issues and he wasn't getting enough to eat at one feeding, so he did a lot of snacking.. every 2 hours. now he's on formula and is eating more, but still wakes, I'm guessing out of habit) so I've started to put him to bed like normal, but then when he wakes if it's less than 4 hours I'm letting him cry. which is heartbreaking and stressful, honestly. I'm so worried that something may be wrong with him and that's why he's crying. but since starting this last week I've noticed he is extra clingy during the day time. I can't even walk 2 feet away from him while he happily plays without him looking at me and crying. is this a phase? he's almost 6months, is this something new to his age? Does he fell abandoned at night and is scared I'm going to leave in the day? I'm worried "crying it out" isn't the best thing for him. but I do need to find a way for him to sleep alone and through the night. Please, any positive or helpful input is welcomed