Maybe, maybe not
Most likely an "amoxicillin rash
" a non-allergic rash which occurs when Amoxicillin is used while one has a viral infection.
Once the viral infection resolves and Amoxicillin is used again no rash occurs (non-allergic). Patients are commonly incorrectly labeled as Amoxicillin allergic because of this phenomenon. If this was the first time drug was ever used then definitely not true allergy.
Answer assisted by David Miller, Medical Student