The word from Jeff Fisher via the medical team is that Young likely has a torn flexor tendon in his thumb and, if so, will likely require season-ending surgery.
The issue with flexor tendon injuries (as opposed to extension tendon injuries) of the hand is that they will often retract further into the palm if not surgically corrected. And the sooner these are operated on, the less retraction you have, and the better the outcome.
Medical staffs are always hesitant to give a certain diagnosis on the sideline unless x-rays in the locker room show an obvious injury or the sideline exam is similarly 100% without doubt.
It is likely Young will have an MRI within the next couple days to confirm or refute the diagnosis. But if it's confirmed, expect Young to be out the rest of the year. Head coach Jeff Fisher indicated in Sunday's post-game press conference that he has lost his starting job even if he does not need surgery.