Card game where you organize your hand
Seems you're thinking of Rack-O.

In Rack-O, you have a deck of 40-60 uniquely numbered cards, and start by filling your 10-card rack with them in a random order. You then take turns replacing cards in your rack with either the top card of the discard pile or deck, and the first player to get their cards in ascending order wins. If I remember correctly from playing it, you can't rearrange the cards in your rack either.