My 4 year old has an average heart rate 115-120. Has a sleeping rate 88-92. Actitivity rate 118-125. A week ago had a cold. Is this normal?

A little on Higher. side. A young children tend to run higher HR than the adult.but usually less than 100. If they are active and their HR can be 110min. However if he/she is just sitting and listening to the story and running 120/min HR, she needs to be checked out by her Doctor. Does she have Bluish discoloration of her lips? Does she get SOB easily? Some of the symptoms you can keep eye on.