Well, first of all, the gluten thing is not an allergy. If you have celiac, that is an autoimmune disease. And if you don't have celiac, but a sensitivity to gluten, that is called non-celiac gluten intolerance. The difference is that with celiac there is intestinal damage, and with NCGI, there isn't. It seems obvious to me based on your response to the diet that you have one or the other.
Also, be aware that celiac runs in families. You probably should both be tested. That would mean going back on gluten because the tests will show false negative if you aren't eating it. These are the tests you should ask for:
tTG IgA and tTG IgG
DGP IgA and DGP IgG
total serum IgA control test
AGA IgA and AGA IgG (older less reliable tests)
And it is not uncommon to see improvement so soon. It usually takes a long time (months, and in some cases, a couple of years) to see complete healing, but most people see enough improvement within days to let them know they are on the right track.