In the future, here's a good set of guidelines to follow, I'm also not a lawyer this is just things I've learned over the years:
1. Never use their equipment for any personal projects.
2. Never install anything on their equipment for personal projects, even if it's to help them.
3. If you want payment from someone for something, then never do any piece of the project without confirmation in advance that you'll receive compensation for the work.
4. Don't do anything if it's not in writing.
The thing is, doing personal projects in your own time is fine and dandy, but already can be rough if you didn't read your employment contract closely as they may own it if you work for them. Using what may have been a personal project during your "work hours" for an employer may give them rights to that work unless you had an agreement otherwise. Beyond all that... if you didn't have an agreement before the work started you really can't expect them to pay for it now.
Now from the summary it sounds like you've just done design and not implementation, you're never going to get extra compensation for design you took it upon yourself to do, but do yourself a favor and just stop right there.