That's "URI" dude: Upper Respiratory Infection
And YES, you want to use antibiotics to kill the INFECTION! Just like in human medicine, KEEP TREATING AFTER THE SYMPTOMS GO AWAY!! Use the ENTIRE prescription that the vet gave you!
I'm not yelling at you, but I don't want to leave any room for misinterpretation here. URI's happen when something about the environmental conditions the snake was (or is) kept in caused the perfect environment in the tissues of the respiratory tract for a bacterial bloom (infection) to occur. Antibiotics are very good things, eventhough a lot of people like to try to paint them as evil - there's a whole other reasoning there, and it's not worth getting into here. The point of finishing the medication, even when symptoms have gone away, is that even without symptoms being apparent, the infection (blooming bacteria colony) can still exist - and will bounce back if the treatment stops early. If the infection relapses like that, then the remaining antibiotic won't be enough to treat the subsequent infection, and there is a fair chance that the bacteria will become slightly resistant to that medication. That is why you need to keep treating even after the symptoms go away.
Once you've killed this infection with antibiotics, you'll need to make sure that this doesn't happen again... unless you enjoy paying the vet. The way you ensure your snake stays healthy is to know what temperatures it is being kept at and what the relative humidity in the cage is. If the temps are too low, and/or the humidity is either too high or too low, another URI could occur once the antibiotics metabolize out of the snake's system. If you've already checked and re-checked your temps and humidity and they are not at fault (and post a thread here and ask if you aren't sure), then you should be able to console yourself that your snake didn't get sick because of something you did, and you should be able to look forward to many years of health in your pet.
I hope this helps. 
~Rebecca
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0.1 Dumeril's Boa '04 (Courtney)
1.2 Ball Pythons
[1.0 '05 Orange Hypo (Specter)]
[0.1 '05 Het Orange Hypo (Sylvia)]
[0.1 '03 Normal (Sue)]
0.2 American Pit Bull Terriers (40lb darling lap dogs:Brandy&Mara)