Final answer:
Dimmesdale's refusal of medical aid and his belief in his unworthiness to walk with God suggest he sees his suffering as deserved penance for his sins within the Puritanical context of the story.
Step-by-step explanation:
When Dimmesdale refuses medical aid by saying, "I need no medicine," and that he does not think himself worthy "to walk" with God, he is insinuating that his suffering is deserved, the consequence of his sins, and that he is unworthy of the divine grace or the redemption it might symbolize.
This self-denial and belief in unworthiness stem from the intense internal guilt and the Puritanical religious context within which he exists.
The acknowledgment of his sins, yet refusal of aid, points to a spiritually inflicted wound rather than a physical one, that he believes cannot be healed by mere medicine. Instead, he sees his suffering as penance that he must endure to possibly attain salvation, reflecting the Puritan value of inner spiritual experience over external remedies or actions.