I'd suggest getting a sling or carrier. If that's what he needs, then the best thing is to hold him, but a carrier will mean your hands are still free. They go through these phases, it's no unusual at all and it will pass.
You may well find that if you meet his need to be held, he'll sleep better, and the clinginess will also improve, and the sleeping will improve more, and so on.

It's quite normal also for them to get unsettled around the 3-4 month mark as their little brains have a big developmental leap about this time. It's liable to leave some babies needing more reassurance.