I can be defensive and even mildly jingoistic about America

The US has one of the most effective brainwashing systems in the (first) world, patriotism-wise. I suspect that a part of it is the historical narrative of a real or imagined success against formidable odds, all in the last 200 years or so. The message "America is great" is also constantly all over the school system and the media. This is really hard to resist, no matter how often you repeat to yourself "I ought to keep my identity small".

I've been wondering lately whether it would be closer to the truth if, instead of thinking of myself as Jewish (ethnically), it would be better to frame it as "People kept telling me I was Jewish until I started believing it".

I heard that sentiment many times, not necessarily from people of Jewish descent, although the latter are an easy example. Jews in the early 20th century Germany thought if themselves as Germans, until "real Germans" disabused them of that notion in 1930s. Same happened in Russia in 1950s. Various Yugoslavian ethnicities suddenly realized in 1990s that they were not just Yugoslavians, but Serbs, Albanians, Croatians etc., and those who did not were quickly and forcefully reminded of it by their neighbors.