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

This may be some sort of a contact rash and, if so, can easily be treated with topicals in most cases.  Have your doctor take a look.

HI,   Have you been wearing any type of head garment? Sometimes, those can cause itching and a rash. Antibiotic ointment and dressings can do the same thing. It would be best for you to see your PS to determine what is going on,Best,Dr. Christine Rodgers 

Changes to the skin soon after a facelift is always a concern. The skin has had the blood supply reduced and the facial flaps and incision lines are under tension. This can lead to problems and bad scarring quickly. A correct diagnosis by your surgeon is important to get the correct treatment.

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.

HI
    it sounds like you are having an allergic reaction to something. It is important to remove the offending agent... a topical cream or ointment that you are using, a dressing or a medication. Once it is removed it is possible to treat with an antihistamine and oral steroid if possible. See your surgeon or a dermatologist asap. 
Dr C

This type of rash can be treated by allergy type preparations as well as antibacterial preparations.   This rash also mandates that your doctor take a look at you and see if larger problem.   My Best,   Dr Commons