In heads a prepositional phrase constituting an adverbial of location within a relative clause headed by that:
I will look totally stupid in it >>> that I will look totally stupid in _
If the relative pronoun were that instead of which, the preposition could be 'pied-piped' instead of 'stranded':
in which I will look totally stupid
But this is not permitted with that.
Stranding a preposition in this manner was once frowned on by many stylists, but this prejudice is gradually disappearing. Stranding has always been common in colloquial registers (although recent corpus studies* suggest that it is not nearly so common as was once thought).
* Johansson and Geisler, "Pied Piping in Spoken English", in Renouf, Explorations in Corpus Linguistics, 1998; Hoffman, "Variable vs. categorical effects: Preposition pied piping and stranding in British English relative clauses", Journal of English Linguistics, 2005; Hoffman, Preposition Placement in English, 2011.