Both phrases work better with the verb "to do" as an auxillery as we commonly use in American English:
"Until when DO I need to use everything?"
"By when DO I need to use everything?"
Another phrase is "until what time DO i need to use everything"
Also, I would not use "everything" in this specific instance, I would say..:
"Until when DO I need to use it up?" ( "it" is the commuter ticket and all of its contents)
"By when I need to use it up?" ( "it" is the commuter ticket and all of its contents)
"Use it up" is a phrase commonly used for something that is singular but consumable.
For example: I had a collection of bags/pens/notebooks/candles, but i used it up (means they were each used and now there are no more)