I once had a therapist who called that very same thought process by an interesting name: monkey mind. Another one called it a "thought attack." Think of one bad thing and your imagination will take off down the twisted corridors of "what if".
Rationalization is a good step forward, as is recognizing that the thoughts you are having are irrational. The easiest way to stop a thought attack like that is to recognize it really early and firmly tell yourself no. The earlier you can stop the thoughts from racing towards you, the easier they will be to manage. If you catch yourself mid-stream it is much more difficult to break out.
One thing to think about for the future is the productivity of the thoughts. Anxiety in general is, for the most part, non-productive. For example: say one of my friends has not come over yet. They don't have a cell phone. Thoughts come racing in about all the hundreds of thousands of terrible things that could have happened to them (or that they have in store for me). However, all of these thoughts do not change what is going to happen. In fact, it may actually make things worse as when they actually do arrive 30 minutes late I will be highly excitable and agitated.
A lot of the things you can do to prevent these thought attacks is to lower you overall level of anxiety and stress. There are multiple books on the subject you could borrow from your local library. If you are less anxious overall your thought attacks won't have as much fuel with which to fling irrational, troubling thoughts at you.
I am glad that everything is okay with your parents. I hope you can find a way to reduce your anxiety.
