Can my players abuse this homebrew Blade of the Thirst magic item?

I am designing a homebrew magic item. I think I have it balanced but need to know if there are any loopholes I have not seen.

Blade of the thirst, magical longsword, requires attunement, versatile, finesse.

Concept:
The weapon of an ancient vampire lord, the blade of the thirst is imbued with the vampire’s lust for blood.

Description:
A black longsword with a guard made up of 3 carved black roses; the guard is gripped thorned vines that extend from the roses and bind to the wielder’s wrist.

Features:
Blade of the thirst confers proficiency for itself onto the wielder.
At the start of the wielder’s turn the blade of thirst drains blood from its wielder, causing 1/2/3 damage to the wielder (player’s choice); the sword counts as a +x weapon until the end of the turn, where x is the damage caused to the wielder.

  1. Is this magic item balanced?
  2. Is there an obvious way to abuse it?