Axel Schuessler, in his ABC Etymological Dictionary of Old Chinese, writes:
wǒ 我 (ŋâ[B]) LH ŋai[B], OCM *ŋâiʔ
Independent pronoun 'I, we' [OB, BI, Shi], in classical texts 'I
(stressed), we'....Originally, the graph for wǒ seems to have been
created to write the name of a Shang period people/country, 'sheep' 羊
was later added 義 (prob. signifying pastoralists) in order to
distinguish the name from the pronoun.
He cites Sagart TP 81, 4–5, 1995: 328–342. (Probably this article, though I'm not sure.) This doesn't mean the graph doesn't originally depict a rake (as proposed by Richard Sears of chineseetymology.org) or a saw-toothed weapon with a long handle (as proposed by Ash Henson and co. at the Outlier Dictionary), but it does suggest that in any case, by the time it was 假借 borrowed for the pronoun, it was apparently already used figuratively to refer to a country or its people.
Schuessler goes on to say that Mandarin wǒ is a colloquial archaism; some northern dialects have the expected ě, while some southern dialects have preserved the Old Chinese rhyme shown above.
Key: LH = Later Han, OCM = Old Chinese Minimal, OB = Shang dynasty oracle bone inscriptions, BI = bronze inscriptions, Shi = 詩經 Shījīng (therefore, appears no later than 600 BC), TP = 通報 T'oung Pao (a Wade-Giles-ish rendering), a journal on traditional Chinese culture founded in 1890. The pronunciation in parentheses is the Middle Chinese reconstruction; the [B] is actually a superscript and represents 上聲 shǎngshēng, the second of the four Middle Chinese tones, from which evolved the modern Mandarin third tone.