Why is the doctor saying it's not silent reflux? I hate the reluctance you sometimes hear of to prescribe something for babies. Yes, babies cry, but they shouldn't like my DD1 did, they should be able to lie down occasionally. An adult wouldn't be left like that.
Sorry, that doesn't help you, just a rant. What does your HV say? You may need to push or ask to see a different doctor. Hopefully if you don't get anywhere with the GP it'll improve soon. It's relentlessly hard though, and I didn't have a toddler.
Thank you for your sympathies 
It also used to piss me off no end that people would suggest depression / PND. NO. Parenting small children, especially not straightforward 'easy babies' is a relentless, exhausting, boring, thankless soul destroying, hot sleepless mess. It's hard as fuck to the point of impossible at times and I considered running away to start a new life in Guatemala reguarly.
Yes! I was on a thread the other day where the OP was struggling with an 8 week old non sleeping, velcro baby. She got lots of head tilting advice to contact her GP to talk about her mood, and other posters telling her to savour the cuddles.
NO. She needed to be told that it's shit, she's doing well, it will get easier and to just do what she can to get through the day until then. Does my head in.