Build on what you can do, rather than smashing yourself every time you go out. If you think about it, you're trying to run twice as far as you actually can, at the moment.
Since you can 'only' do a mile, I would do a run of just under a mile. When it becomes manageable, THEN put perhaps 1/4 mile onto it- less even. Also, don't be too rigid on the number of days you run at this stage. I would wait until any soreness from your runs has gone before running again.
I would look at a late summer 10K, which should be manageable. Do a park run or two, when you feel ready. These are 5k, so it's a good interim goal.
Well done Aimee, so glad it's going so well for you. I would hate for you to think I was discouraging you in any way, but take it easy for a while, whilst you get back into it. I'm sure you'll be up to 5K and more very soon.
Keep running with your run group. Are they able to offer any advice to you? I wouldn't run much further than about 4 miles until you can do the distance comfortably. Put emphasis on running regularly, perhaps 3 times per week would be good if you can manage it.
On one of your runs, (assuming 3 miles) run the middle mile a bit quicker than normal, with a nice slow warm up and a good warm down. A bit of speed, relatively speaking, will add another gear to your performance.