Because this forum does not allow me to assess the severity of your infection, I cannot judge whether antibiotics are necessary in your case. Please keep in mind that regardless of the fact that antibiotics alone cannot cure dental
infection, it does not logically follow that antibiotics are always unnecessary. In point of fact, your dentist
has me at a disadvantage, as she has had the opportunity to assess your infection, and she chose to give you antibiotics.
Having said that, the improving trend you have experienced in the past two days without antibiotics does beg the question of whether antibiotics are unnecessary in your case. Historically, doctors have over-prescribed and inappropriately prescribed antibiotics, to the point where bacterial populations have developed resistance to them. This is a serious problem, because doctors are having increasing difficulty in controlling serious infections as a result of this phenomenon. In fact the federal Centers for Disease Control has an initiative to educate doctors and consumers when antibiotics are appropriate, and when they're not. See: http://www.cdc.gov/getsmart/
In light of the improvement in your symptoms of infection, it may be advantageous for you to contact your dentist to verify whether the antibiotics she prescribed are really necessary. Giving antibiotics "just to be safe" is not really making you any safer, and may even be exposing you to unnecessary risk. While I don't want to second-guess your dentist, this matter does warrant a follow-up query to her.
Hope this helps. If my answer has been helpful, please remember to click "accept".