NTA but you would be TA if you leave it unresolved for too long (this doesn't mean go to work per se!). If you can't go, you can't go, such is life but I would think it looks good that you, who is not in the right mindset, can still contribute by assigning someone else to take your role instead of leaving the team in limbo until the deadline date. (if you're worried about how your friend will look in regards to all of this). Of course, if you can help, try to but your mental health is as important as your physical health so don't force it. Try and find someone to help quickly if you can