+1 for XCGB and David_R.
If a big bloke walked towards you in the street or came into the pub do you run home or phone 999 just becuase you don't like the look of him and he looks like he "could" be a bit handy?
By picking up your dog you are reinforcing to the dog that he has to be scared of everything and that any dog approaching it is a threat, this is not too smart and can leed to a nervous dog that is likely to feel more scared more easily and possibly snap at other dogs thus actually starting the fight.
My mother in laws precious King Charles gets picked up and kissed at every little thing and is totally unmanagable as a result. I took my new puppy rund to meet her and the first thing she did was go for his throat as she now equates any dog with danger.
I agree that the owner should have called out to you asking if your dog was alright with other dogs or reassuring you that hers was a big dappy thing (assuming it was), but you need to remain calm and assertive or else your dog will pick up on this and start to feel snappy and nervous too. Your calling to her and her not responding was irrsesponsible and she should have headed and responded your call.
On the other hand if her dog was a slavering beast that would eat you dog for breakfast then it was irresposnible to have it off the lead- but if this was the case your picking it up wouldn't have changed anything and it would have attcked both of you- which it didn't.
Getting worried yourself and scooping up your dog just turns it into something far more interesting that the other dog will want to know.
I don't want to sound rude here, I'm simply trying to offer some advice as an experienced trainer of working dogs. Sounds like you could both do with an opputunity to socialise and get to know more big dogs that way you will both feel calm happy and confident when surprised by one. You admit that you were scarred too.
A call to the local RSPCA or Dogs Trust Dog shelter would give you a chance to take your dog and both get to know and get used to some large dogs in a controlled enviornment thus leaving you both calm and happy campers when another big lad comes over to say hello, albeit in a less than restrained way.