I have to mostly agree with Smoove here. The difference between your mile time and mile pace in the 2k is pretty significant, which indicates maybe you were tired going into that 2k, you have moved into a new fitness level, or your endurance isn't there. With the current training of intervals 600m or less, my first thought was that will produce a much faster mile time relative to your 3k/5k mile pace.
I ran a mile/3k double over the weekend on a 200m indoor track, so I think that I have something to add here. My 3k was about 15 seconds per mile slower than my mile, but I found the difference between the races immense, despite the 3k only being 7 more laps or 1400m more overall. To me, running a 3k is more of a sustained, even effort in which you slowly work down the pace in the 2nd half of the race, while the mile is basically racing on the edge past the 600m mark.
First of all, people are going to blaze that first 400m, just hold back and let them go in front of you without worrying too much about position. I was in the slow heat with everyone running 9:30 and slower, and they had to go out under 70. After avoiding a fast start, my focus was to settle into my goal pace of XX seconds per lap, and then pass people on the straightaways. I wasn't even thinking about picking up the pace until the 1600m mark. I broke down the race into 5 lap parts, with the first 5 just maintaining the pace, the second 5 focused on maintaining, passing, and monitoring how I'm feeling, and last 5 making myself uncomfortable and trying to slowly work down the pace. I probably started my kick at 500m, knowing that most people would wait until the last lap and I could slowly increase the pace and pass most everyone before the last lap. Over the course of the race, I probably went from near last to 5m from 1st and then finished 3rd.