This is almost definitely not it, because I'm sure you'd remember the mermaid bit, but I thought I'd throw it out there because of the cover, and the fact that that the second cover page has a close-up of her 'blue face'. Also I do think there is a scene of her going into a tent, but it's on an island not a desert. Sirena - Donna Jo Napoli
Sirena by Donna Jo Napoli was my favorite YA book when I was a teen.