Denise,
I have had a similar experience recently with British Airways.
In the past, your booking would be "held" for a few minutes to allow you to complete - but now its all "real time". You don't actually have a booking until you have paid - so if others are trying to book at the same time as you its a race to complete the booking.
If someone else completes before you and there are no seats left at that price than you have to start again and will get a higher price. Its standard policy for most airlines to change (increase) prices as availability decreases.
Unfortunately this is bound to happen at times like this when lots of people are trying to rebook flights in the same period and the flights are already fairly full.
So, the message is, have everything ready and do it as fast as you can !
Incidentally, with BA, there were no seats left at all so I had to start again with a different airline !
Ian