It does, indeed, sound like blossom end rot, but from what I've read, it's actually rarely the case that the soil being calcium deficient is the cause of the problem. Calcium may be implicated in blossom end rot (but that doesn't mean the soil is deficient).
Here's a link where Carolyn Male (a well-known tomato expert) tells us all about blossom end rot and how most people don't need to add extra calcium to their soil.
Anyway, from my own experience, I gave plants loads of basalt rockdust (which is high in calcium). I even gave them things like calcium nitrate and eggshells. It was a pretty bad problem with several plants, this year, notwithstanding the calcium they had. If anything, I'm convinced that too much calcium can cause blossom end rot, but I could be wrong.
Really, though, the weather seemed to correlate rather strongly with blossom end rot, this year. It was very, very hot, and dry. When it cooled, the plants didn't have as many problems.
I've read on a forum that one person likes to use straw to prevent it (by burying it a few inches below the soil where the plant is). Straw/hay is actually high in nutrients (such as nitrogen) and it may do similar things for your soil as manure. I hear it can encourage good microbes (especially alfalfa hay). It can also act as ground cover. Anyway, that was only one person, but it really sounded like it worked, and it perked my interest enough to tell you about it.
Considering the fruits are small when they're rotting, that reminds me of a Yellow Straightneck squash with the problem I have this year. The squash appears to have a fungal infection at the roots, actually. I don't know if that's related to the problem, but possibly. It doesn't have enough light, though. A lack of light may be your problem.