Help! Injured soleus/lower leg area. Should I try a Nov. tri?

Hello, I apologize for this being lengthy, so only read if you're interested in helping a newbie get some insight into her first sports injury and where to go from here. Because I need help!

Training was going great until a few weeks ago, when I was on a nice run and felt some pain start to build in my left lower leg. Gradually it worsened, to the point where I had to stop running and limped back the 2 miles to my car. R.I.C.E.D and took Aleve for a couple days. Three days later (8-26) I was leaving work (I'm an ER nurse, so it's alot of walking) and I felt this horrendous ripping POP and instant onset of pretty severe pain and inability to walk normally. Limping to my car is my new sport, it seems. WOW did it hurt. It was ok at rest but I was unable to weightbear or walk. Flexion and extension of the foot were also excruciating. I'm sure I tore a muscle back there, likely the soleus. It's a pretty distinct feeling, and a first for me. I went to an urgent care, they wouldn't see me and said I needed a specialist. I didn't get in to a doctor for diagnostics (try getting a referral to a California ortho when you live in Florida. Out of network, blah blah blah. I hate HMO's.) ANYWAY... Was off work a week, R.I.C.E.D and was able to walk somewhat normally by the end of that week, but any sort of position change or surface level change caused discomfort. I lost almost 3 weeks training.

NOW...I can walk normally, pain free. I can swim. I did a spin class this morning (didn't want to risk limping back to my car AGAIN) and felt GREAT. Afterwards, felt a little spasm, like a rubber band jiggling. Swimming seemed to stretch it out, as I swam after Spin class. But no pain or discomfort at all. Jogging, however, is still an issue. I jogged 11 minutes earlier this week, probably 15 minutes yesterday. I felt some twinges of discomfort and would stop. But I was taking it VERY easy, my thinking is to VERY gradually try and progress.

So I'm not sure what to do from here? My tri is on Catalina Island in November. While it's not what I WANTED to do, it seems to me that I can walk the final event, and still have an enjoyable experience. But i'm getting alot of feedback from other people (not triathles) that I'm unrealistic and going to risk further injury.

So what I'm asking (FINALLY, i know) is if anyone has experienced this, and feedback on if they think it's realistic to try and complete a tri in November. And without giving "medical advice", any stretching and strengthening pointers are appreciated! Thanks!