6 weeks is PLENTY of time to get in shape, you've got a great base, it takes more than a week or two to really lose fitness.
Your fitness will come back faster if you go slow now. It's counter-intuative, but if your lungs were involved it's especially true!
Weights don't tax the lungs, so lift if you can (but not to the point of severe soreness), but don't push the cardio hard. I got the full blown flu during marathon training last year, I was down hard for 8 days, but was back on track w/in 10 days. I started back super slow, walked on the treadmill, then run 5 minutes walk 1, and so on, but it came back pretty fast. As you've found, trying to come back right away results in soreness that just puts you back farther.