If 'B' has TTF forecasting, I'd be checking that, and if it indicates a change to conditions below the alternate minima, then, yes, you do need an alternate. If you don't have the fuel to go anywhere, then I guess it's a PAN call and some paperwork afterwards.
What sort of hazardous WX are you talking about?
If 'B' is only covered by the original forecast, but the actual is as you describe, then a decision is required based on other airport availability and remaining fuel.
Again, it comes down to where else could you go.