The most frequent problem we see with beginning runners is breathing while running. In 95% plus of these cases it's from running too fast for the runner's conditioning. I suspect this is the case with you. Even though you think you're not running very fast, it's probably faster than your body can manage at this beginning stage.
At the same time, I agree with James Grove. Because of your age and your "health was not good for many many years", you should have a good physical if you haven't lately.
"Do or do not. There is no try." Yoda
11/13/2011 Harrisburg Marathon 4:08
10/9/11 Harrisburg Half Marathon 1:40:41
11/24/2011 New Castle Turkey Trot 5K 21:22
8/6/2011 Attack the Gap 10K 49:19
4/17/2011 CVRT 15K 1:14:53
Its always a relief to get the doctor's "okay" for a strenous sport like running. When I started back running a few years ago (after taking a long hiatus) I also had a stress test and the doctor told me "run and train all you want, you're good to go". It was music to my ears!
As far as the anemia, if could definitely affect your running even though you don't notice it in your day to day activities. I donated blood a couple of years ago and afterwards felt perfectly fine. I didn't notice any difference in my regular activities but for a few weeks afterwards I felt SOOOO fatigued when I ran. Not out of breath, like you're saying, but just dragged out and listless. So yeah, anemia could be a factor. Hope you get that resolved!
T- low iron will surely affect your breathing! Your red blood cells MUST have iron in order to bind oxygen. If you don't have enough iron to help out those red blood cells, they really do nothing for you. So, your cells say "hey, I'm not getting enough oxygen here!!!" Then your respiratory system has to ramp up the breathing in order to compensate. The problem really is, if you don't have enough iron, all that work your respiratory system is doing is for no good. Bottom line... you must get your iron up if you want your body cooperate!
"Spectacular achievements are always preceded by unspectacular preparation" ~Roger Staubach
Started C25K - April 18, 2011
Graduated C25K - June 17, 2011
Started Hal Higdon's Half Marathon Program - June 19, 2011
First 5K - July 2, 2011 Time: 34:21
2nd 5K - August 13, 2011 Time: 33:18