I did everything you said, jcarlilesieu, and the problem has improved. Th noise is for the most part gone... it is absent for a few minutes and then I hear it again for one second. The water is slightly dripping out of the filter, not pouring out like it did before. But at least its moving to some degree.
Now the fish is sitting up near the filter where the water is dripping out, she already seems a bit happier. The violent one is still in the net.
Thanks for all your help regarding the filter. I'm going to get a tester kit on Thursday (which is the very earliest I can possibly go, and I hope that won't harm the fish.) I have class all the rest of today, and all of tomorrow. Now that the filter somewhat works, I hope these two fish can just hang in there.