OP - looking at your results you are definitely under medicated and showing typical hypo symptoms. GPs usually only look at your labs and will pretty much ignore how you feel (wonder if they'd be so happy to do so if they were the ones affected!). So you can feel at death's door but if your TSH is within range (a very stupidly wide range where many are actually ill) they won't do anything. Your TSH is 2.9 which is too high, it needs to be around 1.0.
Your FT4 is way, way too low, no wonder you feel dreadful, it's just barely in range. They haven't measured your FT3 (the active thyroid hormone). That's because labs make the decision, if your TSH and FT4 are 'in range' then they won't measure FT3. I'll bet yours in on the floor as your FT4 is so low.
Also, you've the typical low ferritin so commonly seen in those with hypothyroidism - you need to up your iron intake either by eating more red meat, or supplementing (probably best with a non-heme iron source as that's more readily tolerated).
Re your heartburn. You don't have high stomach acid, please don't take antacids. You have LOW stomach acid (very, very common amongst those with hypothyroidsim) and as such won't absorb your nutrients very well. There are a number of ways to help with this. You can try taking dilute lemon juice or dilute apple cider vinegar about half an hour prior to meals (increases stomach acidity). You could try taking Swedish Bitters (liquid form, very bitter herbs taken just before a meal to stimulate stomach acid). Or you could take Betaine HCl (can find on Amazon) with meals (with food or just after). Try one capsule with a meal, if that's not enough to prevent heartburn, raise to 2 capsules, and so on.
Just another note: you said taking more Levo made you 'head towards hyperthyroid'. Your GP isn't correct. To be hyperthyroid you'd need over range TSH, FT4 AND FT3.
It will be very, very hard to convince your doctor that you need an increase as they'll be fixated on labs. Your only recourse is to source and buy Levothyroxine online (easy enough to do) and try increasing yourself, and doing your own labs to monitor by finger prick blood tests. Otherwise they will, in effect, be keeping you ill.