Yes, I recommend you see your doctor.
Hi, welcome to the forum, yes, your condition seems to be allergy related and is suggestive of Atopic dermatitis (AD), which is a chronic inflammatory skin diorder. There is abnormal barrier presents in the skin which gets disrupted upon exposure to the allergen. It is quite unusual to be present on one half of the body.
The allergen can be in the form of excessive bathing, low humidity environments, emotional stress, xerosis (dry skin), overheating of skin, and exposure to solvents and detergents. Avoiding these situations is helpful for acute flares as well as for long-term management.
In such condition maintenance of adequate hydration of the skin is quite important. Which includes thick creams (eg, Eucerin, Cetaphil, Nutraderm), which have a low water content, or ointments (eg, petroleum jelly, Aquaphor, Petrolatum), which have zero water content, are better.
Along with above measure use of anti histamines and corticosteroids will help to reduce itching of the skin as well as rash.
Rash can also be due to certain infections, the possibilities are tick-associated rash illness, lymes disease, viral- measles, chicken pox, rosella, leptospirosis etc. Serological tests may be needed to rule out above mentioned disease (not necessary if allergy is confirmed).
I suggest you to consult dermatologist. Take care and regards.