"May napansín akong butas sa aking medyas." doesn't really mean "I noticed a (there's a) hole in my socks."
A more direct, albeit awkward, translation would be, "I have a hole in my sock that was noticed (presumably by me)."
There is a relative clause hidden in there: "napansing butas (a hole that was noticed)"
If you want to convince yourself that is a relative clause with 'butas' as its head, try adding 'hindi'.
May hindi napansin akong butas sa aking medyas.
Notice how it means, "I have a hole in my socks that wasn't noticed."
Also, to further convince yourself that is a relative clause, try moving the head to the beginning of the clause, which is statistically more common in tagalog.
"butas na napansin (a hole that was noticed)"
Notice how the meaning and nuance are exactly the same as the original sentence.
May butas akong napansin sa aking medyas.
Relative clauses can be tricky in tagalog because, unlike English and most other (all?) European languages, the head doesn't have to appear at the beginning of the clause. It can come at the end, like Korean and Japanese, or (gasp!) even in the middle.
This confusion is exacerbated by the syntactic demand of "may" that, if the possesser is a pronoun and the thing possessed is a relative phrase, the pronomial possesser must come after the first word of the following relative clause.