"$20 or less" doesn't buy you much these days, even in Nicaragua. What you could find, I'd question how clean and safe the places are. I used to stay at places like that in Nicaragua all the time; I'm getting older now and I have less tolerance. I fully admit that's at work here.
Are you absolutely limited to spending that amount? You don't need to spend $75 a night, but if you loosen the pursestrings to, say, $35-40, you can buy more comfort, most important, air conditioning. Nicaragua gets VERY hot.
The cheap places just don't deal with booking sites. You'll have to make the arrangements directly, possibly by phone. (They may or may not have E-mail.)
You probably don't need to reserve in advance. You say, "for a couple of weeks at the end of the month" ... I can't tell how far that takes you into September. Sept. 14 and 15 are holidays in Nicaragua. Places will likely be very busy that weekend.