There's much controversy about this matter. Some scientist say the minerals that are good for our bodies are organic minerals or clathrates and that's what plants are for, to "distill" inorganic water into juices that are beneficial to us. Others say inorganic minerals present in the water are essential for our health and that distilled water will eventually cause demineralization of our bodies.
When I was reasearching about this matter I found an interesting article in a number of the New York Times of 1933 by a retired navy medical officer that performed a study of the effect of distilled water on retired senior officers because navy personnel must drink this kind of water since mineral water would occupy precious cargo space. The age range of these officers were in the 60-80 frame and none of the subject had any of the considered usual illnesses of those ages like arthritis, gout, cataract, rheum, etc. They were in a perfect shape for their age but "The New York Times" is not a very trustworthy newspaper so better be careful with that information... lol. And strangely enough when I searched again for that article in Google periodicals I couldn't find it again hmmm. Censorship in Google? naah
A word of advice, studies have demonstrated that distillation process doesn't purify the water from toxins like dioxin, pesticides, herbicides or any other volatile substances so it's best to combine the process with activated carbon filters and others.
From my perspective I can say I've been taking distilled water for months and no noticeable damage to my health have been experienced and neither an improvement and healing like you say in three months. The effects may be noticed after years of taking only distilled water and take into account that those retired senior officers lived a life that required exercise of them like any military career so that could influence in their health too.
Now I'm not taking distilled water because reverse osmosis is easier and more comfortable to use than distilling machines.