Those teachers didn't teach a very good lesson. Poor Betta, glad that you are doing you can help him out. What size tank were the Betta & goldfish in? You've already been given good advice for the Betta, clean, warm water is going to be his best medicine. From the pic it appears he has fin rot. It would be in his best interest to get him a heater otherwise he probably won't heal properly & will continue to have health issues. Or I would see if he can be rehomed away from the school. Now for the Goldfish, if the goldfish is NOT in a at least a 20g tank he or she will not live long or have a good life. Goldies are huge waste producers so they need frequent water changes or extremely good filtration & in order to grow properly need a minimum of a 20g tank plus their diet is a little more specialized than most people think. If the teachers are not willing to house & feed the goldie correctly then he needs to be rehomed.