[RPG] What happens if you say you’re doing Adventurers League, but end up playing a completely home rule thing

If we assume that all spells and items at your disposal restore your health by regaining hit points, and we also assume that all the damage dealt to our hypothetical character was dealt by the Sword of Wounding, it would seem that the character is eternally stuck at 0 HP.

However, let us turn to the "Recuperating" downtime activity listed on page 187 of the PHB (emphasis mine):

You can use downtime between adventures to recover from debilitating injury, disease, or poison.

After three days of downtime spent recuperating, you can make a DC 15 Constitution saving throw. On a successful save, you can choose one of the following results:

• End one effect on you that prevents you from regaining hit points.
• For the next 24 hours, gain advantage on saving throws against one disease or poison currently affecting you.

So, after 3 days you can make a DC 15 Con save to try and remove the effect of the Sword of Wounding from your character. If you fail, you can try again in another 3 days, provided that your unconscious body is actually allowed to have downtime to recuperate (i.e. left to rest somewhere in a bed, while the rest of the party does their own downtime activities). Once you have made the save, you are both:

• stable at 0 HP, and
• able to regain hit points again, meaning that in 1d4 hours you will be back up with 1 hit point (or sooner with potentially more HP if you receive healing).

Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

Emphasis mine.

Consider You and another creature (Zorb). If you are forced to share a space with Zorb, it happens - no shunting in any directions unless something specifically tells you to.
So, if you fail a save against polymorph and are turned into a Large creature (and your new size overlaps with Zorb's space), then you are sharing a space with Zorb.
On your next turn (or Zorb's next turn, if it happens first), you must move to no longer be sharing a space (if it's possible).

That's RAW.

As far as how I would adjucate it: I would make use of the Squeezing rules.

Squeezing into a Smaller Space
A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that’s only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it’s in the smaller space

(thanks KorvinStarmast for the rules text)

I would mandate that you Squeeze so that your Large form only occupies a Medium creature's space (and no overlap happens in the first place), and that you cannot stop Squeezing until there is room for your entire form.

But that is not RAW, and is merely my opinion.