Hello,
As per my clinical experience, itching sensation under the skin on chest and back indicate possible allergic condition with skin sensitivity via IgE mediated immune response. The following guidelines will help for better recovery:
- Keep the area clean with antiseptic liquid or soap
- Wear loose, clean, cotton clothes
- Avoid exposure to prolong or excess sunlight
- Intake of anti histamine as 
cetirizine in mild cases and 
diphenhydramine in moderate to severe cases
- Loratidine or 
fexofenadine are preventive medications before the onset of itching
- Systemic steroids are reserved for severe unresponsive cases
- Control of blood sugar
- Local application of 
miconazole or 
clotrimazole cream in case of skin eruptions or vesicles
Take care. Hope I have answered your question. Let me know if I can assist you further.
Regards,
Dr. Bhagyesh V. Patel, General Surgeon