“Emily in Paris” star Ashley Park revealed on Friday she had been hospitalized while on vacation over the holidays, dealing with a case of tonsillitis that developed into “critical septic shock.” “As I sit here processing and recovering from the first few weeks of 2024, the only word I can think of is grateful,” Park captioned of a series of Instagram photos, which show her lying in a hospital bed with tubes coming out of her nose. The 32-year-old actress, who recently had a pivotal role in Emmy-winning Netflix series “Beef,” went on to explain that she caught tonsillitis around New Years — an…