Ah jeez welcome to a long journey that will hopefully be shorter than ours has been!
My son has been breastfed exclusively til he was 13 months old, but he was so severely sensitive to milk and soy that if I even had a piece of bread that had touched vegetable oil (100% soybean oil)or any milk ingredient(whey, casein) he would scream and scream for a week+. We did not know he was allergic to soy also until he was about 6 months old. If your little one is still having issues even though you've changed to the Neocate, and you've given it a week run with little to no improvement, I recommend trying Elecare, which has absolutely zero proteins/allergens and is more digested than the Neocate, which would help with the IGE if that is what it is instead of an intolerance to soy. The biggest drawback is that the Elecare is extraordinarily expensive. One of the main ingredients in Neocate is soy... so this may be an issue. If you try out the Elecare and it works, some insurance companies will agree to assist in paying for it when it is shown necessary for the child, and there is also the option of Medicaid assistance if your income is low enough, but your husband being a software engineer you probably wont qualify for that one :). The stuff runs about $54 a can, and since it is fully digested they drink it like breast milk, they don't stay as full as long, etc.
It is believed that if you eliminate whatever it is that they're sensitive to in their diet, it will also make the reflux go away...
The medication that they gave you, we also had but it did us no good because he was still getting soy (until we figured out that it was a problem). I do wish you the best of luck on this, and know that there is someone here who has gone through the hours on end of screaming (not just high cries, but screams...), the zero time naps, the constant holding of the baby because they can not sleep any other way, and I imagine you're probably having to cosleep too, for the household to get any sleep. Good mommy vibes and lots of patience sent your way... Please let me know if this helps :)