Is it permissible to take out an interest-based loan to buy medicines and operate a pharmacy, given the existence of other debts, the possession of gold insufficient to cover the costs, and the absence of any other way to operate the pharmacy before the license expires?

There is no necessity for what you mentioned to permit riba (usury/interest). Legal necessity (ḍarūrah shar‘iyyah) is a state of severe danger or hardship from which harm to life, limb, honor, intellect, or property is feared, whereupon committing a prohibited act becomes permissible to avert the harm. As for extravagance in celebrations, or purchasing cars and building houses, or accumulating luxuries, or preparing money for business advancement, these are not true necessities that permit riba. Riba is one of the gravest major sins, and Allah has threatened war against its perpetrator. The Messenger of Allah, peace and blessings be upon him, cursed the one who consumes riba, the one who gives it, its scribe, and its two witnesses. Fear Allah and do not borrow with riba, for lawful alternatives are many.