Is an allergic or heat-rash-type itching on my neck and under my chin normal after a face and neck lift?

It is not normal to have a rash after a face/neck lift but it can occur.  I would say the most common reason for having a rash after the procedure would be from wearing a compression garment after the surgery.  I'm not sure if you were asked to use one or not.  It is also possible that you may have developed a rash from any topical agents that were used during your procedure.  I would recommend contacting your surgeon to see what was used during your surgery to try and determine the cause of your rash and consequently, the treatment.  

Hello,
Itchiness is normal in the healing process. Some cells (mastcells) which are involved in the healing process release histamine which causes itchiness. If you have a rash on your skin, that could be some irritation or allergic reaction. If the rash is only on the operated area but not anywhere else in your body, it could be due to any skin products, garments or dressings. Best check with your doctor.