Teferi's Protection has the clause
your life total can't change
If I get hit with a creature with Infect, what happens?
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Teferi's Protection does work against Infect. You missed a relevant part of the spell's text (emphasis mine):
Until your next turn, your life total can't change and you gain protection from everything. All permanents you control phase out.
This means all damage to you is prevented (rule 702.16e), which also means the infect creature never applies poison counters to you.
Technically, you can still gain poison counters (even through the protection) with cards that don't target players or deal damage such as Ichor Rats or Proliferate effects, or if the infect damage can't be prevented due to another effect (like Stomp or Questing Beast).
As a supplement to ryanyuyu's answer, if Teferi's Protection didn't have the "you gain protection from everything" clause (e.g. if you had controlled Platinum Emperion instead), then you will indeed get poison counters. You are still dealt damage and all effects that trigger upon you being dealt damage still happen. It's just that your life total doesn't change.
From the rulings on Platinum Emperion:
07/12/2018 Platinum Emperion’s ability doesn’t prevent damage. Rather, it changes the results of that damage. For example, if a creature with lifelink deals damage to you, you won’t lose any life, but its controller will still gain that much life. Similarly, if a creature you control with lifelink deals damage to another player, that player will lose life but you won’t gain any life.
07/12/2018 Abilities that trigger whenever damage is dealt to you will still trigger because that damage is still dealt, even though your life total doesn’t change as a result.
From this it's easy to see that infect creatures still do damage, and since infect replaces damage with poison counters, you still get poison counters. Your life total wasn't changing anyway and Platinum Emperion's ability has no effect.