rukalukavina,
I'm no expert but I have a few questions and ideas.
Do you know that your hemoglobin level is normal? If you don't know it would be worth finding out.
Are you staying hydrated? Vigorous exercise can easily leave you dehydrated.
If you are overweight, a regular smoker, or have other medical issues, that can limit your capacity for exercise, although it's still important to do whatever exercise you can do safely.
You may simply be overdoing the amount of exercise. General exercise is good for you, but I'd be worried about exercising to the point where you are short of breath. You may be better off exercising for a short period of time, even if you don't feel yourself getting tired, and then gradually increasing the time, but not to the point where you end up short of breath again. You may find it easier to avoid long sessions of exercise and have multiple shorter sessions instead. You can also do strength and flexibility exercises that don't involve as much aerobic activity.
Even though you are in remission, your forum signature says you are still taking cyclosporine. The amount of exercise that's suitable for patients talking immunosuppressants is still an
area of research so getting your doctor's advice about it would be a good idea.