I have a couple of thoughts:
1. There is no way falling at the start cost you 45-60 seconds. In reality it was a 10sec penalty at most, even if you took your time getting up. If you don't believe me, try counting to 10 in your head right now.
2. Unless you get spiked directly on your achilles, you should just keep running. Waiting 15-20min to get it bandaged up is not going to make a difference, so you might as well run the race. Plus if you finish with blood all over you it looks cool.
3. It sounds like you went into this race with a negative/defeatist attitude from the start, and when 1 thing went wrong you were ready to give up.
4. Your teammates are right to get on your case about this. You may have felt like this race was unimportant, but everyone else was out there racing. By walking off and acting like it didn't matter you came off as entitled and disrespectful towards the team as a whole. I don't think that's what you intended, but that's how they'll see it.
Here's what you should do:
Talk to your coaches. Apologize and explain what was going through your head, but avoid making excuses. Be mature and take responsibility. Then ask them if you can stand up and apologize to the rest of the team. This may be outside your comfort zone, but it'll be worth it. Be sincere, take responsibility, and they will respect and forgive you for it.