I was in a similar situation, but I wanted to run and did. I end up regretting it as it did waste a season of my eligibility and re-injured myself.
From my experience, you will not run well at all. I was in the pool for 5 weeks with a foot injury(most likely a stress reaction/fracture) and plantar fasciitis. I ended up getting out of the pool and two weeks later at conference ran the mile and ended up screwing up my foot again and my plantar fasciitis flared up. I had to take the rest of the spring off and did not ran until June of that year.
If you are not man enough to talk to your coach about it, then I would say fake the injury. But I think that your best option is to go to your coach and say that you are not in shape and that you are worried that you will re-injure yourself by running the 3k at conference. I would also point out that your PR would not score and that you are not in PR shape (which most likely is the case if you have been in the pool for weeks). By approaching your coach you own up to your actions and show respect to your coach and hopefully they will reciprocate the respect and not make you run.