Do not administer antibiotics without a vet diagnosis, you can make problems worse by doing this, or not be treating them at all. Seriously, not a thing to trifle with
1. Antibiotics are designed to work against specific bacteria- you need to make sure that you have an antibiotic that affects the bacteria your tortoise has.
2. Antibiotics do not affect viruses, fungi, etc. so do not work on a lot of common problems tortoises have.
3. Many antibiotics have side effects, such as liver stress, etc. that you need to know about and balance against the original issue.
4. Mis-use of antibiotics makes drug-resistant germs that are harder and harder to control. Lots of common bacteria in the world are now resistant to lots of safe antibiotics because of misuse.
And of course there are things like determining the right dose, figuring out the right way to get it in the animal to do the necessary job, etc.