What the dentists prescribed you were antibiotics. Having rashes from any kinds of medication, not only antibiotics, would mean that you are allergic to those medications. Rashes/itchiness/ or worst, breathing difficulty after taking a type of medicine warrants medical attention. You should go and see a medical doctor and tell them that you get allergic reactions from taking the medications. They will investigate further before you are diagnosed to be allergic to the medication. You should then remember the name of the medication and always tell your dentists/medical doctors before they prescribe you any medications.
I have seen some people saying that they are allergic to some medications because they get diarrhea after taking them. This is not allergic reactions, this is side effects from taking the medications. Side effects of medications can be found at the label/box.
Next Steps
SImply stop taking any medications that cause you rashes/skin itchiness.