Aww hardly Millie's fault, just one of those things!
Tbh we'd have carried on with the walk, Minnie gets in any water she can.
The sea is usually pretty cold by this time of year (not so this year) and we do limit her time in there, but we did check with the vet when she was about 2 and swimming a lot, and she said they're fine so long as it's not for too long at a time
Sounds like you came out of it worst off