I can see that is white spot. Due to gold fish need very cold water and the cold water will caused the white spot parasite active. Beside that, gold fish create lot of waste which will increase the ammonia. And this will kill yr betta.

I think you need a tank which is around 8inch x 8 inch x 8inch at least for yr betta. Quarantine it with anti white spot medicine n some salt. Try to use heater to increase the temperature to 30C. Try to increase it 1C a day.