I've been sick with a "cold" for about a week. i've noticed my heart is beating really fast (103bpm). i also have asthma. can the "cold" cause this?

Yes. : And in various ways. Fever raises heart rate. Decongestants, both those taken by mouth like Pseudoephedrine and those sprayed in the nose like oxymetazoline, can speed up the heart. If your asthma is acting up your heart rate will increase. All of these are good reasons to see a health care professional as soon as possible.

Possibly....: The upper respiratory infection could be causing inflammation in your airways resulting in bronchospasm. Is your heart beating fast all the time or with activity? The bronchospasm could be leading to a drop in the oxygen level in your blood causing your heart rate to increase. Another etiology is your bronchodilator inhaler which can cause an increase in heart rate as a side effect.See your doctor.