I know this turned into a physics discussion (which makes sense) after awhile and now most people have probably already decided this conversation was over but I just wanted to update everyone on my progress (two days later, that is).
I put a bike computer on so I have a better idea of overall speed and distance. It doesn't tell me much, just the basics. No heart rate monitor or anything like that.
The daily ride I'm doing is a mile and a half. I do it about 30 seconds shy of 10 minutes, most of the time going about 10 mph. I tend to get a bit tired towards the end, but already not as much as I did the day before.
This is actually a longer version of the ride that was making my legs burn. Now after riding, there's a little soreness but it's gone fairly quick. Not even 30 minutes later and really, I just like my legs need a good stretch. I've tried my best to incorporate the advice I got here and I think it's really paying off. I attempt to keep a really steady cadence and I think I'm doing pretty good. A lot of times, it just feels like my feet are going with the flow. I'm still getting used to being back on a bike so sometimes I get too distracted with other things to keep track of my cadence like I should.
After a ride, I'm not winded at all. Saturday and Sunday, I came home gasping for air like a fish out of water. Today, if I got on the phone right after getting off my bike, no one would be the wiser. Also, I found myself wanting to keep going and I would have if I didn't have to go to work.
So anyways, thanks for all the advice! It has been a tremendous help.