What are your water parameters before and after your water change? Usually, problems with gills, it's due to water quality. Also, have you added aquarium salt into your tank to help with your Betta's respiratory distress?
BettaFix actually might make it worse, because BettaFix has been known to cause issues with Betta's labyrinth organ.
API makes antibiotics in powder form, which is easier to to divy up for smaller tanks than the crushing pills. You can try Amoxicillin, Tetracycline or Sulfamethoxazole. I have all 3 in my fish first aid kit, and they worked for me when I needed them. However, I'd like to stress that you need to check your water parameters first before doing antibiotics, because if that's not right, antibiotics won't help.
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