Great answer Ben.
If you have a temperature you will usually notice an increase in your pulse rate, and now add the anxiety and your have a increased pulse rate.
Try not to over think you pulse rate and let yourself go back to sleep. Your pulse will settle back down with rest if you let go or the "what if's"
If it is truly a worry for you, please do check in with your physician.
Take care and drink fluids for the cold.