Hello,
Welcome to HCM,
Your allergic conditions has lead to decreased immunity and has make you more vulnerable for bacterial infection. You may be having secondary bacterial infection which as lead to infection of the throat causing difficulty in swallowing.

As you are having bronchitis it has lead to irritation of the mucosa of the throat and causing the symptoms like cough and constriction of the bronchus.
Chronic irritation of the throat can also leads to difficulty in swallowing.

I would suggest you to avoid the triggering factors which precipitates the episodes of asthma.
I would suggest you to follow
1.Salt water gargling
2.Oral antihistamines
3.Oral bronchodialators
Your symptoms will improve with these remedies, if it is not improving you may requires chest X ray and blood examination.
Thank you.

Hi i read ur problem that u have asthama and chronic bronchitis with constant cough all the day,everyday.U also tell that u have trouble in swallowing the saliva. First i ask u that u take any other medicine like aspirin?because these drug can pasipitate the attack of bronchial asthama.The pasipitating factor the disease are allergens,emotional stress,infection,cold ,pollution etc. So u should be prevent these factor.For investigation CXR,PFT.CBP(complete blood picture) for infection and level of ur asthma and bronchitis.Second u have trouble in swallowing the saliva.U confirm that u have difficulty in saliva or food. There will be chances more of upper respiratory tract infection.In my opinion u take only hott water ,avoid the cold climate by using sweater and coats. U take one glass water boiling with 5-6 leaves of tulsi,ginger,piper nigram(kali mirch)when extract comes in water then cold and drink . This process doing everyday.u also take Chavanprash an ayurvedic medicine which provides more relief.so u met ur doctor for chekup and investigation and follow my precaution which i tell u.U should not worried and take precaution. Hope this answers your query. WISHING YOUR GOOD HEALTH