pochen
to throb
A strong, rhythmic beating or pounding, especially of the heart or pulse.
Nach dem Sprint pochte sein Herz wild in seiner Brust.
After the sprint, his heart throbbed wildly in his chest.

to throb / to insist
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to throb
A strong, rhythmic beating or pounding, especially of the heart or pulse.
Nach dem Sprint pochte sein Herz wild in seiner Brust.
After the sprint, his heart throbbed wildly in his chest.

You can recognize the meaning of 'pochen' (to throb / to insist / to pound) from the sentence structure. If it refers to a bodily sensation, it often stands alone or has the body part as the subject. If someone is demanding something, 'auf' + accusative follows. If someone is knocking, 'an' + dative follows.
Sein Herz pochte vor Aufregung.
His heart throbbed with excitement.
In the meaning 'auf etwas bestehen' (to insist on something), 'pochen' is always used with the preposition 'auf' and the accusative. This structure is fixed and indicates that a demand is being made.
Die Gewerkschaft pocht auf eine Lohnerhöhung von fünf Prozent.
The union is insisting on a five percent pay raise.
When it is about rhythmic beating in the body, the typical subjects are 'das Herz' (the heart), 'der Puls' (the pulse), or 'die Schläfen' (the temples, in the head).
Nach dem Treppensteigen pochte ihr Puls spürbar am Handgelenk.
After climbing the stairs, her pulse throbbed noticeably at her wrist.
When 'pochen' (to throb) describes pain, the subject is often an injured or inflamed body part. Typical examples are 'der Zahn' (the tooth), 'die Wunde' (the wound), or simply 'es' (it) in an impersonal sentence.
Die Wunde an meinem Finger pocht seit Stunden.
The wound on my finger has been throbbing for hours.
In the meaning 'klopfen' (to knock), 'pochen' is often used in literary or older texts. It can describe a stronger or more insistent knocking than the neutral 'klopfen' (to knock).
Der Fremde pochte mit seiner Faust gegen das schwere Holztor.
The stranger pounded with his fist against the heavy wooden gate.
to hit / beat
'schlagen' and 'pochen' can both describe a rhythmic sound or rhythmic movement. For the heart, 'schlagen' is the normal, neutral word: 'Das Herz schlägt' (the heart beats). 'pochen' emphasizes that the beating is strong, clear, or unpleasantly noticeable. You also say that a wound or your head 'pocht' when the pain pulses rhythmically. With a door, 'pochen' can mean loud, repeated knocking, but it sounds somewhat stronger or more noticeable than normal 'klopfen' (to knock). Learners may confuse 'schlagen' and 'pochen' because both work with the heart. 'schlagen' is neutral, while 'pochen' emphasizes strength or an unpleasant feeling.

Seit dem Sturz pocht die Wunde an meinem Knie.
Since the fall, the wound on my knee has been throbbing.
Nach dem Lauf schlug mein Herz sehr schnell.
After the run, my heart was beating very fast.