Hi intense mucosy cough ad what you say appears more like upper respiratory infection with an element of allergy. For confirming this wil havto rule out sinusitis nasal block with post nadal drip or tosiltis. Cardiovasclar failiure pnemonia and bronchitis have to be ruled out at physical examination .i suppose there is no fever. Esr raised high could be because of pregnancy per se and also due to dilutional anaemia.once cofimed will give you a cough expectorant anti allergy medication if not better a n inhaler. Will think about giving antibiotics only if you have fever or coloured sputum.