You'll never embarrass yourself if you're out running - you're always faster than the guy sitting on the couch.
If you can run 6 miles in 42 minutes, that's a 7:00 minute pace, which is excellent. I agree with COTW, you seem like you could easily shoot for a sub-7 pace, especially with a few more weeks/months of training, depending on when your race is. Depending on how much you want to train, I'd recommend doing at least one long, easy run per week, ideally up to 9 or 10 miles if you can, as well as one tempo run per week, where you run a shorter distance but at a pace faster than your race goal pace.
The best way to get faster is to add distance. If you can run 15K easily, then a fast 10K gets that much easier.