I hope you feel better . I thought that amoxicilin and penicilin only by proscription. I thought that everything over the counter without amoxicilin and penicilin. May be i am not right. I am working in doctor office and i will ask the doctor. I am just curious. I hope you feel better.
I want to say something about your 5.5 gall tank. Please don't get mad. You don't need to cycle tank if it under 10 gall. and without filter. For 5.5 gall without filter you need to do 1-50% and 1-100% water changes.
There is recommendation from some people on the forum to do this way. I do 100% water changes for my 2.5 gall every 4-5 days.
The forum recomendations for 2.5 gall 1-50% and 1-100% water changes a week. For 5 gall 50% every week and 100% a month. But i think because you have 2 girls in 5.5 gall you need to do 1-50 and 1-100% a wk.
I think it will be also easier for you even after you put gravel i think it easier to change like that instead of vacuum the gravel.
Try that it really good . I do 100% water changes all the time since i get first betta. And it also good because you get all debris out.
Also i know some one who live in Canada. She also has sick betta and she bought aq salt . I will ask her which store she found it. I know we have it in any pet store. Just in case you might need it in the future.
Have a good night sleep guys :)