I would totally panic if I got a phone call like that, I don't have hands free in my car as I have a bit of a phobia about answering the phone so couldn't cope while driving. It goes back years to when my mum phoned from France to say my dad had died and she was stuck in the middle of nowhere with no money and no place to stay!
So I think you did the best thing by trying to stop thinking about the house until the morning - not too much of a hangover though I hope! I suspect it will take a while to sell the house, even if you get it on the market in a week or so and get an offer straightaway, it will still take a while for surveys etc to be done or mortgages to be confirmed. I was a cash buyer, buying an empty house, so was in a position to push for a quick deal but it still took 8 weeks to sort everything out.
Could you consider putting your things in storage for a while and renting a room on a short term lease while you look for somewhere permanent?
I dread having to sell my mums house as she has been living there for over 60 years and the thought of getting rid of all her things makes me exhausted! And I suspect it won't be too long before we will be doing it.
I'm not sure where you live but in most places there seem to be pockets of areas where housing is a lot cheaper than places close by - or at least there are in large towns and cities. My daughter rented in Liverpool and Manchester and because she owns two horses, she's always lived in cheap accommodation - clean enough but not in the best areas! She has just bought her first house, a two bed terrace for only £98,000 in NE Manchester, about £300,000 cheaper than if she lived near me!