You pulse goes up when you have a fever. The rusty coloured mucus should be checked by your doctor. You may an infection in the lungs.
If it is indeed flu, it will take 7 -10 days to clear up. A slight increase in heart rate such as yours is normal when the body is feverish or stressed by illness. As for the cough, that's typical with flu since it's a respiratory illness. The rusty sputum could be blood tinged. Hard coughing could break tiny blood vessels in the throat and discolor the mucous.
If this continues for too long, if the mucous amount increases or if you're having trouble breathing, see the doctor ASAP. You could develop pneumonia and will need treatment.
BTW, your question ended up on the bird forum so I'm going to have it moved to the proper place to get more information.