The reason you get the "unknown column 'sweenster'" error is because it is not in single quotes so mysql tries to treat it like a column name but since there is no column name, sweenster in table users it complains.
This should fix your problem:
$query = "SELECT * FROM users WHERE username=\"$user\"";
EXPLANATION:
You have to escape, the quotation marks, otherwise php will treat it as the end of a string which it recognises as a set of charachters enclosed in quotes.
The dot operator acts as a string concatanator and joins two or more strings together.
Fixing these two aspects (as in the code above) should correct the problem.