Hehe so you think I look stupid..?
I don't, I just have my music on, look straight ahead and keep going. I know when you're jogging you think everyone is looking at you but they're not.
Just stay inside your own head and focus on a target to run to. One of the easiest ways to screw up a run is to be distracted so get into the zone and ignore everyone around you. Pick a target and run there and back. The next day pick something a bit further away.
Remember the techniques from c25k, if someone sees your head above a hedge they should think you're walking, don't bounce about too much. Keep it slow and steady. You will pick your pace up eventually.
If you think you're going to stop, repeat 'keep running, keep running, keep running....' In time with your stride. That will get you through the temporarily tough bit.
On a long run I find 3-4k the hardest. Every time, it kicks in at 3k and mentally it's tough cause there's a long way to go, but magically it gets better again. Now I know that's my weak spot and I do the 'keep running' mantra to get through it.
If you are worried about speed there are techniques to build this up over time but you really need to have the distance/endurance first and then start on timing. But it should be a personal goal, not just because you think you look daft! It's very unlikely that you do.