I clicked on someone's well in March... can't remember the exact date. I clicked on someone else's well today (April 1), and it says "Don't be greedy. You already received a prize from someone's well this month."

Do I have to wait 27, 30, or 31 days to click on another well?

Yeah, exactly that, I think it counts the days by date and checks if around 30+ days passed until your next wish.

Just like @Daneyed said you have to wait 30 days.

I wish the message would give an indication of how many more days 'til you can click again, because I cannot remember when I clicked that well! Mayhap that's a suggestion I should put in the suggestion section.

Yeah, that could be a pretty good idea to add, or unless you want to keep track of days on a calender :)