I usually tell people to focus on the distance first, speed will come later. If you are at that point, then I'd start doing some sprinting during your runs. You mix up sprinting and regular paced running to increase your overall speed. It's called Fartlek:
http://en.wikipedia.org/wiki/Fartlek.
Congrats on the personal best. If I were you, I'd increase my mileage until I was somewhat comfortable running 3 miles. Then, I'd find some 5k races in your area. There is nothing that increases my pace like running in a race. Without even thinking about it I run faster then I would if I ran by myself. It's likely a primal instinct thing. Maybe it's an Alpha Male thing brought on by the sight of Women / Girls in tights?
Once you finish a race or two, look up the results based on your age group. After seeing that you could have beat the guy in your age group who placed one spot ahead of you, if you only ran 10seconds faster each mile, it becomes obvious that you could do that. Think about it, 5,281 feet in a mile, 10 seconds faster over that distance. It doesn't sound that challenging. If you are running a 10 minute mile, that is 600 seconds. Does running a 590 second mile sound unreasonable? Basically, you are looking for a fair challenge. Don't try and race against guys who are running 8 minute miles, go after the guys who are running 9:45 minute miles. Then chase the guys who run 9:30 miles. Etc, etc...
When I was running the summer run series (a weekly 5k put on by a local running group), there was one guy who used to look out for me each week. He got beat by me once early on. I took third place and got a ribbon, he took fourth and got nothing. He made it a point to always know where I was so he could keep up / pass me. We had a great comraderie every time we ran together. Of course, he had let me know that he was looking out for me. So, everytime I saw him pass me or even just get near me, I had another reason to run faster. It got to the point where we'd run behind the other guy and look to overtake him near the end, so he couldn't get back in front. As I said, it was a great experience and really gave me reasons to kick up my pace a bit.