Finger wound - can I work out?

I (26F) accidentally cut the tip of my finger off last week with a rotary blade. Luckily didn’t get down to the bone - just flesh. I went to urgent care and they cauterized the wound and I’ve been wearing a bandaid and a brace to avoid it getting hit. Definitely still hurts like a bitch but I want to get on with my life and routine, which includes getting back in the gym. At least to do legs or something.

Should I be waiting until it is healed to avoid bacteria from sweat? Is there a way I can dress it to make it ok?

They gave me a tetanus booster when I was there and a prescription for an antibiotic in case it seems to be getting infected, but I have not started it yet as I have not had concerns.

If I shouldn’t go back to gym yet, how long should I wait/at what point in the healing should I see as an ok to return?