Hmm... Can't you call in sick? Your health is way more important than your work (at the moment, of course).
I think that there's no point if you go to work beforehand, just to be exhausted as soon as you're in the hospital.
Can you leave the meeting if it's taking too long?
Do they throw you out of the program if you're late?
Take care,
*leaves sugar free chocolate milk in the thread* (I'm from switzerland, so... We have the best chocolate

)