"I'm not as out of breath already" which means you can already see the progress.
Just remember there is absolutely nothing wrong with stopping for a breather, or walking for a bit.
The main trick for improvement is to keep riding. Set yourself a goal of "at least four days a week out of five" commuting by bike, and if you get to Friday with only 3 days, then make yourself ride especially if you don't really want to.
Speed will come after stamina, so don't focus on speed.
Commuting gets a bit boring after a while - you can also mix up your route for variety and interest. A boring ride is less interesting.
Now and again, consider pushing yourself in terms of distance. You can do 2 miles every day for a week, so do a nice slow 4 mile ride to somewhere else in the weekend... go visiting someone.
Get your bike checked over too - even personally I've not noticed gradual deterioration, and then when its fixed its like a personal tail wind!
- tyres properly inflated
- chain lubed and clean
- wheels spinning freely (no brake rub)
- saddle at correct height.
I don't know about your weather, but for me leaving home slightly cold works, because I warm up with the exercise. Overheating is no fun.