Kirsten, I for one KNOW that you would not have been able (physically or financially) to pick up a sick kitty. If I were in your EXACT shoes, I would talk with a shelter for advice.
As for picking up a cat that might be owned, I do not know how it is in Germany. Here, where is it frowned upon to have your cats roaming, I would not even give a thought as to who might miss her (after all, she is sick and roaming the streets). If it were England where I know most all cats roam, I would have different feelings.