Dead Sea
I have Psorasis and was at the Dead Sea a few yrs ago. I dont think you need to organise a specific tour package. I simply went from Jerusalem by taxi having picked up a flight in london, There are hotels nearby which you could probably find online easily enough. And, given the political situation in Israel,and its effects on the tourism industry there I dont think you'll have a problem finding a free room at a good price. By the way, if you do decide on a taxi , haggle and agree price before you go. Come to think of it, haggle for everything in Israel!