There are two main theories of training for endurance.
The first can be characterized as
build a good base of endurance fitness, then do strength and speed work.
The problem many have with that is that the first part, build a good base of endurance fitness, requires long hours in the saddle (sometimes called slow distance rides, or LSD).
The other way is championed by books (and many websites). The most famous book is
The Time-Crunched Cyclist, 2nd Ed.: Fit, Fast, Powerful in 6 Hours a Week
Book by Chris Carmichael and Jim Rutberg.
This approach can be described (in a very simplified way) as using repeated, short, high intensity training sessions to get rapid training results.
While this second approach seems to be the answer to your question, when you mention time constraints, I have two observations to make
- such high intensity training is, IMO, intended for cyclists who already have a pretty good base level of cycling strength and fitness.
- you have already developed an injury.
So, I think this high intensity approach is not for you yet.
Just ride, as much as possible. Don't aim for speed, aim for hours in the saddle. Rides of two hours would be ideal, but I understand that may not easily fit your life style. IMO, this comes down to choices.
You may have heard "if you want something to improve then measure it". So keep a training log. Keep track of hours on the bike and distance (per week). And days per week you rode. You should see your hours increasing, and the distance increasing faster - your average speed will get higher.
Don't worry about blips in the graph, it's the overall trend that's important. Besides, a slack week every now and again will help keep you fresh and motivated. One way of keeping this log is to automate it by using an app such as Strava, Map My Ride, Endomondo, etc.
Be creative to add a few little detours to your normal routes, to add interest and distance. Gradually build the distances, and also a repertoire of rides that you can choose from. Occasionally exploring a completely new route can be fun. Such a ride would often be a slower pace; you shouldn't be riding flat out all the time, or even most of the time in this phase.
Finding a buddy to ride with can help with all this also.
After some months of this approach, you should have a pretty good level of cycling fitness. Then you can mix in some longer, harder rides, and short high intensity work. Make sure you warm up and cool down properly for these, and check out the many websites and books (including the one above) about interval training.
Enjoy. Look after that injury before doing anything else.