Take baby to doctors- clearly something bothering them as they should be settled mostly !
My son was like this as well. Later realised after going to the go that it was gas and him being too hot as im always dressing him up in the house. I started giving him gripe water after each feed and that helps him release gas and poo with ease he is a very happy baby now. So definitely get him to the doctors.
That doesn’t sound right, maybe they have a milk allergy or an upset tum, babies don’t cry like that for no reason though, especially at 4 months, it sounds like more than crying for comfort. Could it be hunger? I’d go see a GP or HV for advice
Also if it’s temporary and just happening now then it’s probably the sleep regression. If you get the wonder weeks app it explains periods of fussiness and when they need extra comfort etc, so that might help
How are they sleeping? If they’re fighting naps due to the sleep regression or not sleeping well at night being overtired can cause a lot of crying. My little man was crying for a couple hours before bed for about a week because he was just point blank refusing to nap after 12 noon even though you could tell he really needed it.
Could be silent reflux or CMPA? My baby would sob for hours and not be put down and he is now on omeprozole and prescribed formula and he is like a different child! So happy