IS 120 a high pulse rate for a 44 year old woman?

The textbook value is 72, at rest. The most important factor affecting your heart rate is your physical condition. Athletes can easily have a heart rate of 55 at rest, and the better your physical condition, the slower your heart rate tends to increase.

Heart rate over 90 may signal an underlying cardiologic condition, so if this is the case, see a physician.