Toenail Fungi

About a month and a half ago I cut my large toe wrong.
I cut very deep into the toe on the outside part of it.
it swelled up and a black bumb formed.
It is very painful the toe has been growing very slowly and is now just underneith the swelling.
I saw a walk in docter who perscribed a weeks worth of mild antibiotics (sorry don’t have the name) and told me to soak I hot water.
The was 3 weeks ago and the swelling hasn’t gone done.
Plus im in school so I have to wear shoes which is probably a perfect enviroment for the bacteria.
Anyways just wondering if you have any tips to reduce the swelling and pain does salt water work better?
I’m going to see a different doc in a couple of days hopefull i’ll get some better results.