12c., a shortening of Old English ic, the first person singular nominative pronoun, from Proto-Germanic *ek (source also of Old Frisian ik, Old Norse ek, Norwegian eg, Danish jeg, Old High German ih, German ich, Gothic ik), from PIE *eg- "I," nominative form of the first person singular pronoun (source also of Sanskrit aham, Hittite uk, Latin ego (source of French Je), Greek ego, Russian ja, Lithuanian aš).
Reduced to i by mid-12c. in northern England, later everywhere; the form ich or ik, especially before vowels, lingered in northern England until c. 1400 and survived in southern dialects until 18c. It began to be capitalized mid-13c. to mark it as a distinct word and avoid misreading in handwritten manuscripts.
The reason for writing I is ... the orthographic habit in the middle ages of using a 'long i' (that is, j or I) whenever the letter was isolated or formed the last letter of a group; the numeral 'one' was written j or I (and three iij, etc.), just as much as the pronoun. [Otto Jespersen, "Growth and Structure of the English Language," p.233]
The dot on the "small" letter -i- began to appear in 11c. Latin manuscripts to distinguish the letter from the stroke of another letter (such as -m- or -n-). Originally a diacritic, it was reduced to a dot with the introduction of Roman type fonts. The letter -y- also was written with a top dot in Old English and early Middle English, during the centuries when -i- tended to be written with a closed loop at the top and thus was almost indistinguishable from the lower-case thorn (þ). In names of U.S. highways (by 1966) it is short for Interstate (adj.).
fem. proper name, Medieval Latin, from Old High German Ida, which is perhaps related to Old Norse ið "work." As the name of a mountain near Troy and one in Crete (the mystic birthplace of Zeus), it probably is a different word, of unknown or non-IE origin; related: Idaean.