What you've described is wrong on many levels. Here's why:
First: There are two broad classes of infections: Bacterial and viral. Antibiotics work only on bacteria. They do nothing for viral infections. Common colds, most of which are a variant of rhinovirus, are viral.
Two cold-related infections that antibiotics can help with are strep and bacterial pneumonia.
Strep usually manifests itself as a terribly sore throat and small white dots on the back of the throat. You can see them with a flashlight. Strep isn't always in the throat. It can be on the tongue, on the lips, in the nose, or even outside the nose as a visible sore. As I recall, the most common form of flesh-eating bacteria (which often begins with an injury to a hand or leg) is a form of strep.
Bacterial pneumonia (and pre-pneumonia) is accompanied by discolored mucous - usually green or brown.
In those cases, you need an antibiotic. But if you've got a common cold, flu or ordinary bronchitis, if your mucous is clear and if you don't have white dots on your throat, you probably don't need antibiotics.
Second: While VERY powerful antibiotics will have you feeling better that day, the common varieties don't work in a day or two. They normally take 3 to 5 days. If you think a day or two of amoxicillin is curing you, it's likely because of one of the following:
1) It wasn't a cold.
2) A placebo effect. That's where you assume it's helping, and therefore you feel better.
3) You were about to start improving anyway. This is the best bet. Colds usually only stay at their peak for a couple of days, so if you wait until your cold is at its worst, in two days more you're going to feel better whether you take an antibiotic or not.
Third: If you only take antibiotics until you feel better, colonies of the bacteria that had a little resistance to the antibiotic will survive. You'll then suffer a relapse, or your immune system will kick in and expel the colonies. You'll think the day or two of antibiotics wiped 'em out, but you'll be mistaken. The next person to contract them will be combating a slightly tougher bug. If he does the same thing as you, the person after that will have a really serious battle.
The responsible thing to do if you don't want to breed antibiotic resistant bacteria... bacteria that are now killing people... is to only take antibiotics when you definitely have a bacterial infection, and to take them until the bacteria being targeted are completely wiped out. That's much longer than it will probably take you to feel better.
Now you know why doctors are reluctant to give you antibiotics. They obviously think your infection is viral. And they realize that antibiotics have been used inappropriately for so many years by so many people that formerly curable conditions are now lethal.
*IF* antibiotics stop working, the average American life will be 30 years less (because lots of kids will die.) That's a big deal.
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