There really isn't anything I can add to the great advice everyone here has already given, including about going clipless.
I just want to add my encouragement that I think when you get set up with clipless pedals, even on this bike, and then a new bike...and then if you do the types of workouts everyone here has recommended...well, I think you are going to improve very rapidly and feel terrific.
If you are riding a heavy steel hybrid, without clipless pedals (and it sounds like without even cages), and you are doing some hilly rides at 12-13mph...I think you are doing great.
Keep at it!! I admire you for doing Tri's...I have not yet had the courage!
"The best rides are the ones where you bite off much more than you can chew, and live through it." ~ Doug Bradbury