Most of the time, sore throats are caused by viral infections. So, your antibiotic would not have an affect on this. Viral upper respiratory infections will often start with a swollen and painful sore throat and fever, then other symptoms will show up as the sore throat starts to feel better.
Your throat can still swell even if you don't have tonsils. The tissues and mucous membranes in your throat will swell just like tonsils would.
Since you have had these symptoms for about 3 days now, I would expect it would start feeling better within a day or two. For the discomfort you can use very warm water, 1 cup mixed with 1/2 tsp salt to gargle (it really does work). Or, throat sprays and lozenges made for sore throat. You can also alternate ibuprofen and acetaminophen to help with pain for short periods of time (less than a week).
If your fever and sore throat does not improve within 2 days, you should see a doctor, perhaps there is an Urgent care clinic in your area.
You should always have a culture and sensitivity done before taking an antibiotic to prevent creating drug-resistant infections later. Antibiotics should only be used for bacterial infections. Viral infections will not be affected, and will run their course anyway.
The best thing to do with viral infections is symptom management (pain in this case), and support your body with adequate rest, good nutrition and fluids to help the infection clear as quickly as possible.
Your tonsils are part of your body's immune system, and will often take on an infection so your body doesn't have to. When your tonsils are removed, there can still be tonsillar tissue left in the throat and/or the other tissues in the throat will continue to do this. So you get sore throats, but often do not have other symptoms of the viral infection.
The way to decrease these infections is to boost your immune system. The best way to do this is to take care of your body, so it can take care of you:
Get enough sleep.
Get some sunshine on your skin everyday, and at least a little exercise every day. Walking outside with bare arms and legs is good for this. This elevates your natural Vitamin D
Eat nutritious foods only. We could all improve on this. Whole grains, low fat dairy and lean meats, more legumes, nuts, seeds and fresh fruits and vegetables.
Drink plenty of water. We all forget about plain water sometimes. In addition, cut out soda pop or anything laden with sugar.
Reduce sugar and salt.
Vitamin D supplements can help improve immune function.
If you don't eat right, a good multivitamin with some extra Vitamin C won't hurt.