The wounds of Merry and Frodo by the Nazgul were very different which is the reason as to why Frodo never got over his wound.
Merry's wound was just as a result of stabbing the Witch-King which was healed fully by Aragorn.
Frodo's wound on the other hand was one designed to draw him into the world of shadows, which it almost accomplished as said by Gandalf in Rivendell. The fact he was almost drawn into that world was the reason he was able to see Glorfindel as a shining light, and the reason why he could never fully recover in Middle Earth.
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His sword was long his lance was keen
His shining helm afar was seen
The countless stars of heavens field
Were mirrored in his silver shield
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