Thanks a lot for your valuable suggestions.
That's a good question.
Technically, you can donate.
Depending on the severity of your asthma, it may not be a good idea, because the oxygen carrying capacity of a unit volume of blood will be decreased. So it depends. Certainly if you do so, for the next month make a good effort to maintain control over your asthma. Despite the drawbacks, it might pay to take 10mg of prednisone evfery day for a month following the donation to insure you don't have a life-threatening attack. After a month, when you replenish the blood, go back to the inhaled steroids.
Generally speaking about 1/54th of your blood volume is re-generated every day, so you will make up the donated blood in a short time.