Opposite idiom for going with the flow

How about "going against the grain"?

https://en.wiktionary.org/wiki/against_the_grain

I believe swimming upstream is about as opposite a sentiment as you can get. It even means the opposite in the two phrases' literal sense.

If you don't go with the flow then you go your own way or do your own thing. Admittedly, for your sample sentence, go-my-own-way personality might be a bit cumbersome. So you may prefer independent or independent-minded:

[independent-minded in Collins Dictionaries:] self-reliant and seeking autonomy

-minded in Cambridge Dictionaries:

having a ​particular ​character, ​interest, or way of ​thinking about things:

She's very ​[] independent-minded (= she has a very ​[] independent ​character).

So, to see how it sounds in your sample sentence:

I have had to come to terms with a lot of cultural differences which has been a struggle for my independent personality.

I have had to come to terms with a lot of cultural differences which has been a struggle for my independent-minded personality.

The common idiom bucking the trend appears to fit your scenario:

to be ​obviously different from the way that a ​situation is ​developing ​generally, ​especially in ​connection with ​financial ​matters

To adapt this into an adjectival form you could say you have a trend bucking personality or, in nounal form, that you are a trend bucker. Both of these words do see usage, as evidenced by google searches - we see that:

Trend-bucking women are living longer