You allowed yourself to get hit 3 times in a row by a Vayne as a squishy. Vayne has weak early game, except if you allow her to free hit you and you cant lock her down.
As for the weak early game, let me clarify that. Compared to most ADCs, Vayne has a very short attack range and no wave clear and that translates to her "weak early game". If you keep her away from you and harass her she has pretty much lost her laning phase. And playing Caitlyn+Janna into Vayne+Soraka you do just that. Stay at max range and poke her when she tries to cs. But you literally walked right into her phase. But she can still dish out huge damage if you dont respect her.
Now look at Vayne in top lane. Compared to most top-laners who are melee-short, she has a range advantage which completely removes her "eak early" simply because she can harass you.
"Weak early game" is a combination of some factors: range disadvantage, early dueling disadvantage, wave clear disadvantage. But because Vayne has a range and wave clear disadvantage doesnt mean she cant out-duel you if you walk onto her face.