I was prescribed Nexium for daily heartburn during a period right before I was diagnosed hypo. After I discovered that I was probably hypothyroid, that the heartburn could be caused by that, and that goiter is a rare but possible side effect of Nexium, I quit it.
I am not saying you should quit it, however. You sound as if your acid problem may be worse than mine was, and only you know how much you can tolerate. If it helps you, you should probably continue to take it.
If your acid reflux is caused by your hypoT, it will get better after your levels improve. (Mine did, but that doesn't mean I never get heartburn now. Just not nearly as often.)
If it isn't caused by hypoT, improved levels won't help. We - and I include myself - too often blame every single thing we have wrong on the thyroid. Try to resist that temptation, because it keeps us living in a dream state where we believe that everything can be cured if we just reach that "magic" dose. Only the things caused by lack of thyroid will get better after the thyroid is optimally replaced. Just because a symptom can be caused by thyroid doesn't mean it always is caused by thyroid.
Ideally, you want to take thyroxine apart from everything. But I know that Nexium has to be taken an hour before eating, too. That makes it tough to take both. If I remember right, you can also take the Nexium 2 or 3 hours after eating, can't you? Maybe you could work it in between breakfast and lunch? If that's impossible, I would reluctantly take them together. The Nexium doesn't contain calcium like other antacids, and so won't bind up your thyroxine like they do.