8:30 AM PT -- Kim just thanked the doctors and nurses who helped Saint, saying, "I just want to thanks every nurse & doctor out there who works so hard around the clock. We are so grateful for you all!"

Kim Kardashian and Kanye West's son, Saint West, was hospitalized last week with a bad case of pneumonia ... TMZ has learned.

Sources tell us the 2-year-old was brought to an L.A. area hospital Thursday with pneumonia, and that his parents were with him while he remained hospitalized, sharing overnight duties.

We're told Saint was released on Saturday, so he was checked in for just a couple days. He's at home now, and sources say he's doing well.

Kim shared a family photo from Christmas just a few days before Saint was admitted.

Kim and Kanye also shared a New Year's Eve kiss on Sunday. The hospitalization went down right after her mid-week meet-up with J Lo and A-Rod -- where Kim and co. enjoyed a taco Wednesday party.

Good thing Saint's on the mend ... his new baby sis is supposed to be coming home sometime this month. She'll probably need her big bro to show her the ropes, sniffle free.