Hello,
Fungal infection or Medications for the same has no relation with Covid Vaccine. However as you mentioned, Chronic Hives will be seen in a condition called Urticaria. A person having specific allergy towards vaccine or vaccine components alone is not supposed to take vaccine. You on the other hand can go ahead with a physicians guidance and it's better to have emergency medication if in case urticarial response is present.
Next Steps
Go ahead and take vaccine
Risk versus Benefit ratio has to be noted, hence it has to be taken
Health Tips
It is best if emergency medications are kept ready. Take the vaccination in a Hospital setup.