You are doing amazingly, I know it feels like hell every day but it will get better.
Firstly, I have had 2 DCs with reflux, ds2 was horrifically ill. Like you I was feeding every 2-3 hours when he was 12 weeks old so he was gaining weight which meant the HV wasn't concerned. Joy.
I too have a medical condition with fatigue as one of the symptoms and honestly there were days when I just wanted to crawl into a corner to escape the responsibility of it all.
So, if you don't think the gaviscon isn't working don't wait. Get back to your GP and see what else can be done. Ds2 ended up being referred to a paediatric consultant who said he would try a different formula first rather than any more medication. So we went on Enfamil AR, you can (or could) walk into a chemist and order it in, it isn't a prescription formula and that worked for us. SMA staydown is similar I think.
But to help his reflux, he slept on me in the daytime until he was over 12 months old (I was lucky enough to be a SAHM with a very understanding 3 year old) sadly I had no help except from my amazing DH when he was home from work. We sat Ds2 in a bumbo, a door bouncer and he had his cot propped up at an angle with cot props (plastic feet that elevate one end of the cot) because when he lay down he refluxed. I did sling him, and wore him out and about until he was almost 3.
He is now 8 years old and still refluxes. Only at night though and only when he is tired.
We tried the early weaning at 17 weeks as recommended by the consultant, but it didn't help, just made the sick a more interesting colour. How I didn't get put off sweet potato forever I'll never know 
Where abouts are you? There maybe people close by who can help you directly or point you toward groups/services.