I actually laid out two workouts that were supposed to be alternated throughout the week, not just one or the other. But whatever at this point. Dips are not/were not "necessary". And you should've kept the rows, because it was the only back exercise in the group. You should be able to do them at home with a very simple setup (put your feet on a box to make them more challenging if needed)
Like nighthawkz said, it's normal for the dominant side to be stronger and/or larger. Once you begin training with weights, it's something that can be addressed to an extent, but with bodyweight stuff, there's no easy solution.
I kinda hate to say it, but you did this to yourself. By doing push-ups and dips (both of which work the triceps, shoulders, and chest) without any back exercise to balance things out, you probably overstressed the supportive muscles around the elbow. Stopping the dips and adding the rows should sort things out soon enough.
But really, if you've been sticking with the routine for 5+ months, you're almost-definitely ready to progress to a new routine.
If you've been fine all along and it's just a recent issue, I'd probably chalk it up to just losing focus for whatever reason. Balance can be weird like that. Play with your stance, moving your feet in or out to see if it gets resolved.
Also, how many push-ups did you every get up to? How's that bet with your boyfriend doing?