Hal Higdon Half Marathon 12 week program
Gives you some good info & background on what it will take. IMO make sure you get the long runs in one of the days. Then maybe the shorter run on 2nd day and some sprint/intervals work on your 3rd day.
Not sure why you can't train more than 3 days....if so on your Off Days make sure to stretch and maybe some basic bodyweight movements (pushup, situp, squat, pullups) provided you can do them properly. I'd recommend some strength work as you'd benefit a lot but in light of the info you provided and knowing not much about your current physical condition hard to recommend:
Cliff Notes: Follow the program in the link, make sure you don't hurt yourself and in 11-12 weeks (based on your 6 mile, 60 minute run) sounds like you should win your challenge. Good luck.