An infant should see a doctor any time you are worried about his/her health. Babies are more delicate than adults :) But, it is common for colds and illness to cause tachycardia, especially if a fever is present.
We are not a substitute for a doctor, I want to make sure you know that first and foremost. But, who told you that the infant has tachycardia? Infant heart rates are normally between 130 and 150 bpm, so if you are feeling the child's pulse and determining that it is tachy, you may just be making false assumptions about what the "normal" rate should be.
If your child does have a could and cough and you suspect tachycardia, you need to get him/her to a doctor who can diagnose any serious conditions. Infections can often increase heart rate as the body is pumping blood and antibodies more quickly through the body to fight the infection. An abnormally high heart rate can be a signal that something much more serious is at play.
Take care,