Oh bless you, I have been where you are very recently. My DD is now 20 weeks and the first 13 weeks of her life were reflux hell.
My sanity was saved by a Moby wrap, you can pick one up for 20 quid on eBay. The material looks daunting at first but there are some great YouTube tutorials that will show you how to tie it on. My baby still takes all her daytime naps in the wrap.
Being upright almost all the time was really the only thing that helped ease her suffering. So sling all day, or car seat or bouncy chair. If she wasn't too refluxy then she could sometimes sleep on a steeply angled mattress, but I often resorted to letting her sleep overnight in her bouncy chair.
Now she can manoeuvre herself about she chooses to sleep on her left hand side. I still put her down on her back but she rolls over herself and seems to sleep a little better for it.
I second getting checked out for tongue tie - DD's was revised at 8 weeks and it helped reduce the actual vomiting, if not the silent reflux. Ranitidine is OK but didn't prove a magic bullet for us. Cranial osteopathy did nothing. Keep feeding little and often, breast milk is much kinder on the stomach too. Dummies can help, although DD prefers to suck her thumb.Only time helped her stomach to mature and stop leaking,and by 13 weeks she was so much happier.
She's now lying next to me, laughing and squeaking to herself - a couple of months ago I didn't think I'd ever see her smile. It does get better, honestly. Good luck.