I'm not sure that an allergic reaction to the chemo drugs would damage the tissues near the port, as it should go into the veins, but I suppose it could happen. I would think there would be other skin areas affected too. It sounds like maybe there is a problem with the port itself (?) Maybe? Are you referring to outer skin tissue?
I had some skin irritation and redness around my port (not exactly sure from what), but my doctor gave me an antibiotic to clear it up. Now it's fine. Obviously, check with your doctor.