Am I being a wimp?

For a week now I have been out of training for two seperated ribs.  The Chiro told me I could train like I always do without further injury, however I find it impossible to get through a session without stopping due to pain.  It hurts to breathe normally much less the deep breaths it takes to complete my cardio workouts.  I can't sleep, it hurts to sit at work and the ibuprofen I take doesn't do much.

I was wondering if anybody has trained through a similar injury and I just need to HTFU and keep going (seems impossible).  Or should I do like I have been doing and wait until it feels somewhat normal?

I have my final sprint tri of the year in 5 weeks and I was hoping to finish in the top 10% overall as I've done twice already this year.  But the injury is really holding me back.  Am I being a wimp?

Thanks,
SHD