So is this a generally applicable rule for possessives? Adding a ת as a binding consonant when the word ends on a vowel?
The ה turns into ת for female objects (חולצה - חולצתי) but is omitted for male (עלה - עלי)
The א is sometimes omitted (אבא - אבי) but not always (כסא - כסאי).
A וֹ (kholam) would add an א, while a ו (vav) would act like other consonants.
A י would act like any consonant.
Why isn’t this “my wet shirt”? Isn’t “my shirt is wet, חולצתי היא רטובה ?
My wet shirt would be חולצתי הרטובה. You can think of חולצתי as החולצה שלי: just as with החולצה שלי, when adding an adjective it must be definite (come with 'ה as a prefix).