Good luck OP. DO NOT BACK DOWN!
Your post has actually made me cry. I could have written it. It took 4.5 months of GP visits and health visitors fobbing me off before we finally saw a lovely GP out of hours who said it was obviously his food. I sobbed with relief - the GP told me I just needed my mum to come and stay as I was obviously struggling to accept that babies do just cry. My health visitor mumbled something about maybe seeing a cranial osteopath and fled after sitting next to me for an hour while DS was in full cry.
The out of hours GP prescribed lactose free formula and said not to worry, our normal GP would give us lots of support and a different prescription of the lactose free didn’t work after a few days. Our GP was rubbish. When I spoke to her she said she ‘didn’t know anything about lactose intolerance in babies’ so we should just get on with it!
The lactose free helped, but DS still wasn’t right so we were prescribed Nutramigen by another GP. My DS was like a different baby.
I have felt so guilty since then that he was in pain for so long. Reading your post reminded me how awful it was. Like you, my DH and family couldn’t / wouldn’t help when they realised how awful it was. When you get this sorted, and you will, be kind to yourself. You have been through hell and you are amazing 
In case it’s still helpful, DS’s symptoms were:
Screaming/ crying inconsolably, especially 1.5 - 2 hours after a feed
Not sleeping (see above)
Snuffly
Constipated / loose nappies but sometimes fine
Eczema patches
Occasionally unexplained rashes
Pulling up legs
Trying to avoid feeds - clearly hungry but not wanting to eat
I now see a brilliant dietician and my 18 month old DS is amazing. Sleeps at night and eats well. Sometimes when he is in pain with teething I can see he panics, so he clearly remembers, but other than that he has no other issues.
I really hope that helps, and you get the support you both need. If you’re worried you won’t, then do as a PP did and sit in the waiting room for an hour before your appointment. That should focus your Drs mind.