Grizzly and Gassy - Help!

Any advice would be hugely appreciated as I am really struggling with my five week-old EBF DS. Unlike my DD, who was jaundiced and was a nightmare to initiate feeding with as she just wanted to sleep, he latched on instantly and has gained weight brilliantly (9lbs 2 at birth, 10lbs 10 at four weeks).

The problem is that he seems to be the most miserable baby in the world! Any time he is awake he is sobbing and will never cuddle in and the only way to stop this is to feed him.

It seems that he would happily feed non-stop but he also seems to be a terrible sleeper - after a feed he will always cry for at least an hour (worse at night) and if he does nod off whilst feeding he wakes up as soon as you unlatch him or move a muscle.
He rarely sleeps for more than an hour and seems to wake very easily.

He has only been sick once but frequently milk just pours back out of his mouth and he really struggles with being burped. He is also very windy and often grizzles and arches his back whilst feeding as if to push things through!

I have tried Infacol and Gripe Water and have cut out dairy for the past week to no avail (not much fun as I am already a coeliac).

I am told he is quite cute but have no idea as I have only seen him red and crying or half his face whilst he feeds. I am really down and embarrassed as he just wails wherever we go and am turning down seeing family and friends as he will just cry unless on the boob.

My DH and DM keep suggesting trying formula but I don't know what to do, as I EBF my DD for a year and wanted to do the same. Any help or advice would be wonderful, as I am really depressed and disappointed after five weeks of sobbing (him and me!)