Sleep has two main phases: NREM sleep and REM sleep. NREM sleep includes deep sleep, during which the heart rate and blood pressure usually decrease. During REM sleep, which is the stage in which dreams are usually more vivid, heart rate and blood pressure can become more variable and may temporarily increase, which is a normal physiological response.
REM sleep becomes longer and more frequent during the second half of the night, so it is quite common to wake up around a REM period in the morning. Therefore, if you notice that your pulse is somewhat higher immediately after waking up, this can be a normal physiological phenomenon, particularly if it settles down after a few minutes of rest.
However, a persistently high resting pulse, especially if associated with chest pain, breathlessness, dizziness, or palpitations, should be evaluated separately.
Next Steps
Consult a psychiatrist.