How can we ever talk about what would be when we must start off by assuming something that's false? A false statement P implies anything, as the last two rows of the truth table for logical implication show.
So then, if we talk about the world as it would be, and not as it is, we find that everything would happen. But everything can't happen. That's logically impossible. This means that it's logically impossible for the world to be in any other state other than the one it is in.
For example, I'm not driving to the store. But if I were, I'd also be swimming, since a conditional statement with a false hypothesis is always true. But I can't drive to the store and swim at the same time! To talk about what would be the case implies a contradiction, and therefore I can never talk about what would be the case. I can only talk about what is the case.
What do you think about this? If you disagree, find the flaw in my argument.
Disregarding the tangents from Fil, we can solve the problem quite easily.
The first flaw is that a false statement does not entail anything. That is what a contradiction does. A false atomic statement entails that its negation is true in FOPL. A contradiction can entail anything.
Also, your example is pretty bad. The statement, "If I am driving, then I am swimming" does not entail a contradiction, not in the least (and this can be demonstrated if you translate the statement into a logical syntax). Perhaps it is physically impossible for me to do both, but it is not logically impossible.
I will not get into possible worlds here. However, there seems to be recurring problems in your line of reasoning:
1) You confuse logic with experience.
2) You do not understand how false statements and contradictions work.
Think about it.