When Molly had kennel cough I thought I was going to lose her. Very scary. It was like not being able to breath and wheezy, labored breathing, and if she moved, she coughed. I think it would sound very similar though if there was tumors in the lung or other problems affecting heart/lungs.
I would definitely have her checked out before letting her mingle with the rest of the gang, just to be on the safe side. Nice that the rescue will cover the cost of that.
Regards,
Sharlene and Molly Muffin