The general advice you hear is to focus just on building your endurance.  I think that's bad advice.  There is no reason why newer runners can't work on speed almost from the day they start running.  Moreover, I think doing so is important for three reasons.  First, I think it helps to prevent injury because it strengthens your muscles.  Second, it adds variety to your running.  Beyond making you faster, variety aids in injury prevention as well because you're not using the exact same muscles in the exact same manner every time you run.  Finally, it's fun.  I'd get bored to tears if I just tried to go out and jog at the same level of effort every day.

Of course, you can't ignore your aerobic development and there is no substitute for putting in the miles.  Moreover, the vast majority of those miles - 75-80% for experienced runners and 90-95% for newer runners - should be done at an easy pace rather than the fast running I just mentioned.  One of the things I noticed in your post is that you only run 2-3 times per week.  It will be very difficult to get much faster on that level of running.  The reality is that running is no different than any other sport in that if you want to get better at that sport, you have to do that sport.  Cycling, fencing, swimming, etc are all great aerobic activities and if what you want is to focus on general fitness, they're terrific but they don't do much to make you a better runner.  To be a better runner, you have to run.  Thus, I would suggest moving to 4 days per week immediately and then to 5 days a week after a couple of months at 4 days a week.

As for speed work, here are some things you can try now and you don't have to go to a track or worry about paces.

1.  Strides - Start these when you have about a mile left in your run.  Over a period of maybe 100 yards, gradually accelerate from a jog to about 90% of all out and then gradually decelerate back to a jog.  The fastest running in the stride shouldn't last more than about 40-50 yards.  Start with 3-4 and work your way up to 6-8.  These work on form and build muscular strength.

2.  Fast Finish - On a couple of runs each week, start picking it up when you have half a mile or so left in your run.  Keep gradually picking up the pace until the last 200 yards is quite uncomfortable.  These teach you to increase the effort even when you are fatigued.

3.  Tempo Run - If you can run 4 miles, you can try this.  Run the first mile easy as a warm up.  Then, pick up the pace to the point where you are running hard but not all out.  Run like that for the next 2 miles.  Run the last mile as a cool down.  Once you work your way up to 5 miles, increase the faster portion to 3 miles.

Hang in there and stick with it.  And don't be a lurker.  

Not much to add but I just wanted to say welcome.

LTH offered some good advice but if you aren't ready to jump into the deep end of the pool yet my 2 cents is:

• Transition from 2-3 days of weekly running to 3-4.
• Keep doing what your doing but add some speed work in just to keep it interesting.
• Keep working  with the personal trainer. Having strength in your core and upper body will help you to be a better runner.
• Don't forget to have fun.

LTH and Scott give great advice.  I wish someone was there to tell me those things when I started in March of 2012.  I went on the "just run more at an easy pace" plan.  I was able to build my miles to a pretty good base, but my pace never really improved that much.  At least, I don't think it did.  You can work on both at the same time.  Adding more days to you week will help too.  Welcome and keep at it.

You are on the right path, interacting and talking running will help with that.

Welcome to the group!

Welcome to the forum.  There are a lot of good people here, who are more than willing to help you improve and cheer your successes and occasional failures.

Moving to an hour of running will help you get to the distance you want. Either c210k, or Bridge to 10k or the One Hour Runner are options.  Running every other day will get you running 3 days one week, 4 days the next.  If you can do that fairly easily, then just run 4 days every week.  When that is easy, go to 5 days.  Increasing your mileage will help both your speed and endurance.  Many years ago I remember being told, 2 days a week is bare maintenance.  3 days a week will see slight improvement.  4+ days a week will see significant improvement.  Cross training is good for developing other muscles and general fitness, and will help you lose weight, if that is part of your goal.  It should reduce the chance of injury.  It can also be a lot of fun.  You're more likely to stick to a fitness program if you're not bored.  It won't really make you a faster runner, just a fitter one.

Welcome, Baconista. I had a BLT just the other day. Where in CA are you?

Welcome to the forum!  Lots of good advice already, so I don't know that I have anything to add, but I will throw in another vote for increasing your frequency.  Oh, and the fun part too, very important.