Yes, this is all good advice - would you please give us an update on your dear little Betta's condition? As you can see on this thread of the Fish forum, although only 2 people have replied to you so far, dozens of fish enthusiasts have read your post with apparent interest!
Did you get a thermometer, yet? It's important to keep his temperature at the appropriate temperature for Betta fish on a consistant basis. The water temperature will be different from the air temperature in the room. It will also depend on the amount of water in his tank because of the size of the tank you provide him with. The 3 cold days certainly could have effected him negatively, but he should be able to recover from fin rot nicely with a little special attention. Fin rot can be cured with frequent complete water changes. Betta Fix can help, too. Ich can also appear in Betta fish sometimes when they have been subjected to temperatures that are too cold for them since they are tropical fish.
First, you should let your little guy get some strength back, though. Yes, clearing the water of the chemicals should be done first, too. This can be accomplished using a Poly Filter and/or an activated carbon filter to help remove what might be left of the medication. This does sound worse than just common fin rot, though. I wonder what else your fish sitters might have done - even if they're not aware of it. If you get a chance, you could read the article on the Fish Site here at BellaOnline.com about how to care for your fish when you are away. Maybe it's safer without the fish babysitters. Sometimes, it's even better to take them with you if possible. They can have a "vacation home" to transport them in.
What kind of pellets are you feeding him? There are various kinds of Betta foods. How
cold exactly did it actually get in the house for 3 days for your little fishy?
Please update us on your Betta. What's his name? What color is he and what does he look like? Is he a solid color or various colors and does he have a pattern on his body and/or fins? I sure do hope he is feeling better.
Please tell us more and we will give you more suggestions.