Possibly severe constipation along with internal parasites--white discharge, loss of appetite, and bloating are very common symptoms of intestinal worms in bettas. The bloating puts pressure on the swim bladder, causing them to lose control over their ability to sink/float/remain upright.
I would put her in a hospital container--for this I use 2 gallon rubbermaid/sterilite plastic storage bins. These are ideal because they are long and shallow, and can be safely heated.
Part of the problem is that your fish is too cold--when a cold blooded animal is kept at a lower temperature than is normal, their entire metabolism slows down, leaving them vulnerable to infections and infestations. It also slows digestion, causing food to get caught in the gut. You need to get a 25 watt adjustable heater and slowly turn the temperature up a degree at a time every few of hours until it gets to 80 degrees.
I would keep the fish in clean, heated water and leave her alone in a quiet, dim place and see if there is any improvement. If there isn't, you should consider using a medication with the ingredient praziquantel. Fortunately, if the problem is internal parasites, fish tend to respond very well to this treatment, in a few days you will see the fish pass the worms (lots of poop!) then the fish will begin eating again. I have had some success with Jungle Parasite Clear.
