There is only one spelling for panic; the verb is inflected 'panic, panics, panicked, and panicking’. The form panick is used for progressive tense, past tense and past participle. We don't write panick today, though English speakers from a few hundred years ago might have (in the same way they might have written musick).
When the alternate spelling “panick” is used for the past participle: "I panicked last night at the disco." When it’s use for progressive tense: “Invariably, when markets are panicking, they sell the stocks quickly.”
It's the rule for root words ending in "c" is that you have to add “k”, so the spelling is related with the pronunciation. If we don't add the <k>, it looks as if the <c> has to be pronounced /s/. If the "k" was not there, “panicing” would look like the word which is supposed to be pronounced as if it is ended in "sing," while “paniced” would be pronounced like “panised”.
One of the milestones that a little boy passed at the age of four or five was the transition from baby clothes or petticoats to trouser or breeches. He would still wear a pinafore to protect his clothes, but he was expected to be able to dress himself and tie the strings of his pinafore in a bow, at the back.