yea I was diagnosed by ENT after a camera down my throat.
I avoided PPIs as hypothyroidism commonly linked with LOW stomach acid already. PPIs would make me worse. ENT agreed and suggested a thyroid dose increase.
I used betaine with pepsin tablets at meal times
Teaspoon of Apple cider vinegar in morning smoothie
No fizzy drinks with meals
Raise head of the bed a bit
Get FT3 higher in range as this impacts the functioning of the valves / sphincters in the digestive tract.
I agree wholeheartedly, sphincters in hypothyroidism of great importance. Probably the whole ‘tone’ of the gastrointestinal tract. Constipation depends on sphincters too. Mag citrate from advice from @SlowDragon helps. Others have mentioned PPIs and their effects. I find if I really do not look after my diet I literally feel a lump in my throat, lots of coughing, producing phlegm, sleep interference and usually finally, a complete upheaval of my digestive tract including reflux. I have noted too that my ankles swell during this upheaval. I have found avoiding sugar is virtually a must for me and a complete adjustment to my eating pattern. First thing is to not get into that situation in the first place if I can avoid it! This means giving food priority number one in my life (thyroid meds off course too). This is more difficult for me than it should be. I get distracted easily. I find something more interesting to do than look after food issues and it requires energy levels with which I negotiate all the time. Food can easily miss out. Reading the forum for example. However many times it happens I swear I won’t let it happen again. I am certain it’s where my inflammation is sourced, certainly upsets area around thyroid especially. A tart apple is a good first aid action (I know not for everybody because they think the ‘acid’ will make it worse). It has an alkalinising effect though actually. You might find yourself burping almost straight after eating. Even just a cup of hot water, with or without lemon will help. However the main thing is avoidance. Decent diet especially including green veg. Maybe a ‘green’ drink if you can try it. I love them. I just wish I was more organised (getting a bit better). I think a life of working too hard interferes with the major things that should get the attention needed. However having a live in chef could be the answer.
He prescribed omeprazole for silent reflux, I thought this was rubbish.
I agree with you. I think 'silent reflux' is one of those 'diagnoses' they use when they have no idea what the problem is - which is often when it comes to thyroid!
Sounds to me like a combination of swollen thyroid (perhaps under-medication?) and low stomach acid. The symptoms of low stomach acid are the same as high stomach acid, so doctors never consider it might be low and treat it as if it's high.
For me, PPIs were dreadful things! They completely messed up my gut. That was ten years ago and I've never really recovered full use of my gut. They will affect your absorption of levo, and just about everything else, because - by the sound of it - your stomach acid is already low, and the PPIs are just making it lower. I would never take them again, myself.
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Reflux 
hypo and reflux
Nutritional recommendations for Acid reflux. 
How to treat bad LPR (silent acid reflux) when hypothyroidism?
REFLUX WHEN UNDERTREATED
