It's a play on an idiom. :) To 'have a frog in your throat' means you're so nervous you can't speak... only croak! You usually get this feeling when the other person is very important, or is someone you're infatuated with. So to overcome this feeling, you "swallow" whatever is in your throat - even if it is a "frog". A similar idiom to "frog in your throat" is "cat got your tongue". PS. Look for "Funny Little Frog" by Belle and Sebastian, it's a great song. ;)

"to swallow the frog" means to do something unpleasant. To overcome your own inner drag. To do a task that is feared or avoided. After you have done this you will feel better. (Caution! We don't talk about swallowing real frogs...) (Or about French. French don't eat frogs every day. Some have never done so.)

it means the person temporarily loses his/her voice or has a hoarse voice