Welcome to the forums and thank you for your post. I totally agree with Geoff here- it is devastating when you've built up the courage to talk to someone and been shut down by someone so ignorant in mental health.
I had to organise a MHCP recently and was also told to think 'positive thoughts'. What I didn't say and wanted to say was that if that worked I wouldn't be here!
To answer your questions, yes- you can choose any psychologist you like and the majority of them will accept a MHCP. Unfortunately though for them to action the MHCP (and get the rebate from Medicare), the referral has to be for them and have their name on it. So unfortunately this means you will have to go back to a GP and get them to adjust the referral, but you won't need a long appointment for this.
and yes - you can absolutely choose any GP you like.
To find a psychologist, sometimes Google can be your best bet as it often has links to their practice and you can get a bit of an idea of what it might be like to work with them - especially since a lot of them have interests in certain topics. You could search something like "psychologist" "(where you live)" "trauma" to help you round this down.
You can also use this website here - https://www.psychology.org.au/Find-a-Psychologist - this will help you round things down too, and then on the left hand side, you can filter more by Medicare > Medicare Psychologist.
I hope this helps. Don't give up. None of this is your fault and it's never too late to get some support.