I would not dare say the distilled water helps with nausea. I've certainly had my days. I will say that the filtered tap water definitely made me more nauseous than distilled or the recommended juices. That could easily be my own personal condition causing that.
Prill beads. Don't throw them away. If you don't want to use them for yourself, put them in your toilet tank in the net bag. That should help the sewage plant. Or put them in your watering can for your flowers and plants. Prill is magnesium oxide. It gives off small amounts of it. You need magnesium. We all do. That is why the prill beads are so good. I also stopped using them; because, it was too much trouble to keep filling the storage container for the water. I kept the container in the garage, no place for it in the kitchen. Then I would fill a pitcher for drinking; and take another pitcher of water out there for the prill container. Just lazy. That's all. That's me.
Distilled water can be found in every grocery store in the U.S. It is less than a dollar per gallon. Too bad you don't have the same situation. They also have gallons of purified water. Since I only use a small amount, distilled is no problem for me.
I don't think you should get a distiller. They are nice; and you can make about a gallon in 4 hours. However the cost of running them is not cheap. It is like having more than 10 100 watt light bulbs burning for 4 hours. In my mind, distilled water from the grocer is much cheaper. The distilled water for auto batteries should be alright. It is distilled after all; but, the manufacturing plant may not care about contamination. It seems that you are better off using your Brita filter, if you are currently not having problems.