It's fantastic that you have found a sport you really seem to love and enjoy doing. I wish I had discovered this at your age! I agree with trying to build up to 4 maybe 5 miles and would also suggest trying some different routes. I bet your Dad would also love to go running off road with you too. I only measure my performance against myself rather than comparing myself to others and I think this is something you could benefit from too.
Well done for your progress so far, the hardest part is getting started!
When I was over 16st I took up Spinning which really helped shift the weight when combined with changes to my diet. I found this was good as it is lower impact, maybe some cross training such as cycling and/swimming could help shift some of the weight?
The Garmins with bluetooth in are able to connect to your mobile phone and then use Livetrack to communicate your position to the people you select. If you do not wish to invest in a new Garmin there is an app available called Glympse that provides the same functionality from your mobile phone. Both systems seems to work well and are great for safety, peace of mind and enabling supporters to find you!