Thanks for providing more information.
Itching without rash can indicate a systemic problem which may include
Liver/Gallbladder or kidney problems
Diabetes or thyroid problems
Polycythemia Vera [too many red cells]
Certain autoimmune diseases [sarcoidosis]
Heavy metal toxicity
As it gets worse after shower so it also suggests Cholinergic Urticaria.
So you need to undergo further investigations like Liver function test,Renal function test,Blood sugar,Thyroid function test,CBC,ESR,Absolute eosinophil count,IgE(for allergy),ESR for further diagnosis.
In the meantime you can take OTC Claritin.
Also apply calamine lotion on body after a bath.
Wear cotton clothes.
As you have cough so you can do saline gargles.
Tightness in chest can be associated with Bronchitis,Acid reflux.
So you can take OTC Robitussin DM and Prilosec.
I suggest you to consult a dermatologist for further evaluation and management.
I hope this helps.
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