I always want to joke when I see the phrase "out of shape" ROUND is a shape too. Seriously though, I am/was in your shoes. First rule of thumb with the out-of-breath when you exercise is to check with a doctor that it is okay for you to exercise. That is really critical with the whole OoB problem.
After getting the okay, I found I was less OofB when I exercise in the water. Start off slowly whether in water or on land. Do 5, 10, or 15 minutes to start and work up to great times. Do what you CAN, rest and then do some more later. I can do more than I used to be able to do and less than I EXPECT to be able to do further along this journey.
I often share a story about someone else - a man I used to watch out my apt. window years back. When he started, he would drive onto the field across the street and get out of his car and walk 1/2 way across (not the long way, just the short way) the field and then back to his car. Soon he was walking all the way across, then half the length, the the whole length, and then one lap around the entire field. After a while he parked his car at the top of the hill and walk down to the track. This process continued for nearly a year and soon he was doing 2 and then 3 and then 4 and more laps of the field and had lost about 150 pounds. He was a GREAT model for me and he was really OUT OF SHAPE when he started, he could barely walk and sometimes even had to stop and rest before returning to his car. I lost track of him because he was no longer easy to spot - he had become fit and was really doing well.