Welcome to just answer.
I am sorry to hear about your discomfort.
If it has been 5 months since the bridge is posing you problems even after mutliple return visits for bite correction than i am sorry to say that there is much more to it than a just a bite correction,or occlusal adjustments.
There can be chances that the bridge is ill fitting one due to which you feel the biting prssure when you eat , which results in pain and discomfort.
also indicates pulpal inflammation,There are chances that the tooth is infected or is decayed.Your bridge may be apparently all right but the tooth which supports brige 'the abutment teeth' (now crowned)may have the problem underlying.
If one or more of your teeth is affected by chronic toothache
,nerve damage could be the cause. Nerve damage may result from teeth tooth decay
or trauma to the teeth through injury during crown
Sensitivity to cold indicates reverssible inflammation but if accompained with sensitivity with hot indicates pulpal necrosis(pulpal death, the living tissue in the teeth).
What happens is that the bacteria penetrates beyond the dentine and inhabits the pulp
!Eventually the nerve dies and has becomes necrotic,spontaneos pain is also present because of the same reason.
Also,it could be just an area of the margin that might be sensitive to the various stimuli.If the crown and cement
aren't sealing the entire marginal areas completely,you could be experiencing sensitivity because of that.The build up of bacteria formed from food acids on your teeth and gums can also become infected if proper oral hygiene is not followed.
Read more about dental bridges here
I will surely recommend you to take second opinion by another dentist who can guide you well, This long standing chronic irritation and pain will only worsen the situation for you.
I feel you should get it replaced if needed,also get the abutment teeth evaluated for any pulp inflammation.
For your pain you can take tablet Tylenol 650mg,thrice daily,it is an otc drug.
Read more about it here.
Feel free to ask any further queries and we can discuss it.Please click ACCEPT if my answer has benefitted you and leave a POSITIVE FEEDBACK.