Get a Heart Rate Monitor, figure out where you fall, with respect to max hr, 220-age isn't great but probably close enough to get a ball park of your effort.
I find riding in a group I can push my HR up higher substantially longer than I feel like I can do on my own with less pain, this is a good data point. A lot of times, you can push a lot harder than you think you can. If I feel like I'm riding hardish but my HR is only running 150 something , I'll push a bit till I'm up closer to threshold, I end up feeling I am working the same, but now going quite a bit faster. Also, ride with people faster than you.
You can check other things that tend to hold people back as well, clothes, cadence, fit. I see a lot of people mashing at <60 rpm and that is how they like it, and they are getting exercise, but they are still slow. slow means low power means less 'exercise' means less calories.
And ya know intervals and stuff, but keep in mind going on feel sometimes lies to you.
A power meter may be nice, but heart rate can give you some indications, at a substantially lower price. You can get a power meter later.
New tires may help but maybe only for a fraction of a mph.