What is the meaning of 冲着 冲 is a word with many nuances. In my sentence, does this 冲着 have any sense of 'rush'? I take '冲着 ...... 去' to mean 'because' here, although maybe 'intent on', 'aiming at' might be better.

当初，你考美元的时候，是冲着美院油画系，但是您现在画的都是国画。

当初，
Originally,
你考美院的时候，
when you took the Arts College entrance exam,
是冲着美院油画系去的，
a) (that) was because you wanted to study oil painting,
b) you were intent on the Faculty of Oil Painting,
c) you were aiming at the Faculty of Oil Painting,
但是您现在画的都是国画。
but now all you paint is Chinese Painting.  

请别冲着我大喊大叫！冲着 = at
海潮冲着峭壁。冲着 = dash against
那幢房子冲着大海。冲着 = faces
其实我就是冲着她来的。冲着 = for
是冲着美院油画系去的，冲着 = because?
冲 is merged from two different characters, 沖 and 衝, notice that 衝 was merged to 沖 and then simplified to 冲 in simplified Chinese. It is very common that using a simple homophone Chinese character replace another complex one in classic Chinese among ordinary people, this is one of the Chinese simplifying rules. We can see the meanings of the characters 冲 or 沖 is about water, yes, it means water (verb), flush, etc. But 衝 is another verb, it means toward (for somebody or something) generally. e.g.: 衝向/冲向: run toward, 衝動/冲动: impulse, 衝着/冲着: for (something).


请别冲着我大喊大叫/請別衝著我大喊大叫:Please don't shout at me.
海潮冲着峭壁/海潮沖著峭壁:The tide is eroding (flushing) the cliff.
那幢房子冲着大海/那幢房子衝著大海:The house face to the sea.
其实我就是冲着她来的/其實我就是衝著她來的:Actually I'm coming for her.
是冲着美院油画系去的/是衝著美院油畫系去的:(Someone) is going for oil painting department of fine arts academy.


The second 冲 is corresponding to 沖 in traditional Chinese, the others are 衝.