The suggested English translation, she gave me a look, is the sort of phrase that would be usually be used only in context, to indicate that she gave me a very deliberate look, with an expression on her face that was intended to communicate something to me (usually something like disapproval, or that I should shut my mouth).
Unless this connotation is present in jag fick en blick av henne (and I'm curious as to whether it is, if any native speaker would care to clarify), I suspect a better (or at least more idiomatic/meaningful) translation might be found among candidates such as she glanced at me, she looked at me, I caught her eye. I'm not sure which...
The reason is probably just that it was hard to think of a straightforward English translation that would also sound good. It seems to me that 'I got a look from her' is so much rarer/more special than 'She gave me a look'. The other ones of course all have more obvious Swedish translations.
Hon gav mig en blick doesn't necessarily have to mean that special kind of look, but it often does. Disapproval is the first thing that comes to mind for me, though it could be something very different too if the context indicates it.