The classical way of analysing for antibiotics is to run TLC with the culture supernatant (initially just plain silica gel with a number of different solvents), then after developing and drying the plates transfer the antibiotic to large enough agar-plates ("stamping") and do an antibiogram to identify where the active molecules have run to. After that, they can be scratched out and analysed further (e.g. by GC-MS or else).
yes, If your antibiotic compound is polypeptide in nature then you can use SDS-PAGE or native page for the confirmation of antibiotic. but the for the determination of structure of antibiotics IR, NMR and GC-MS is needed.
antibiotics produced by bacteria are usually small molecules (< 1kD) so TLC should be better option to separate such small molecules. Native PAGE is good to separate polypeptides larger than 10 kD.
As said by other, unless your antibiotic is a polypeptide you'll not be able to see it.
Even though it is a polypeptide it is likely to be small (under 15kDa) so if you think that you have this type of antibiotic make sure to optimize your separation for small molecules (high % of acrylamide for example).
if it is not a polypeptide the best is to use metabolomics methods to identify your peak and then to characterize the molecule..