We've been playing mtg again lately and I noticed Tainted Remedy. I was thinking what would happen if for example both players are at 3 health, I have Tainted Remedy on the field and my opponent casts Alms of the Vein on me? A draw or do I lose first?

This would result in a draw. Players don't lose QUITE instantly upon hitting 0 or less life. Rather, there's a "State Based Effect" (SBE) that says that when a player is at 0 or less life, they lose the game. These SBEs are checked whenever a player would gain priority (such as to activate an ability or cast a spell), but otherwise they don't come up. In theory, a player can dip below 1 life during the resolution of a spell or ability, and so long as they are at or above 1 life when that spell or ability finishes resolving, then they'll be just fine! In this case, when the SBEs are checked, BOTH players are at or below 0 life, and thus both lose simultaneously.

Thank you, I wasnt sure because it isnt a triggered ability

(They're called state-based actions, not state-based effects.)