Your current CV makes you a viable candidate for a place at each of the universities you mention. Good luck.
Threads such as this are frequent in this forum. It may be that you already know that the answer to your question is "yes".
Most of us seek some degree of affirmation about what we do and who we are. Marcus Aurelius and Montaigne are both quite good on the subject of not seeking plaudits, but being graceful when you obtain them. Rational self-doubt is a good thing, but irrational anxiety isn't. Modesty is a good thing. False modesty isn't.
"Everything in any way beautiful has its beauty of itself, inherent and self-sufficient: praise is no part of it. At any rate, praise does not make anything better or worse."
(Marcus Aurelius, Meditations)
"Virtue is a very vain and frivolous thing if it derive its recommendation from glory; and ’tis to no purpose that we endeavour to give it a station by itself, and separate it from fortune; for what is more accidental than reputation?
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"I care not so much what I am in the opinions of others, as what I am in my own; I would be rich of myself, and not by borrowing."
(Michel de Montaigne, Essays, Book 2, Chapter 6: On Glory