Yep, my pup cried all night at first, then I moved him into the bedroom with us, put his crate right next to my side of the bed, I now use that as my bedside table lol

At 3 months old your puppy can hold his poop in all night. I have a 4 month old here who at 3 months was quite capable of sleeping through the night with no accidents.
I think it's just a case of him being a little stressed out.