Hi.
Thanks for your query and an elucidate history.
Read and understood that you are suffering from
cold and during the severe bout of coughing you felt that the ear exploded, now there is pain in the ear particularly on coughing, swallowing, bending down and there is constant drone noise in the ear.
You are worried whether you have ruptured the
eardrum.
I think you have not ruptured the eardrum as by this time the fluid must have oozed out of the perforation for you to get it at the
ear canal.
This sort of problem occurs when the pharyngeal discharge is forced through the Eustachian tune into the middle ear, accumulating some liquid and you getting the problems like you have been facing.
I would advise you the following:
Take nasal decongestant drops.
Oral decongestant and anti-inflammatory medicines and an antibiotic if you Doctor suggests so.
Please do not instill anything in the ears as this does not help.
Take rest.
Do not blow the nose.
Wishing you an early recovery and cure.