Presumably your respiratory tract infection was bad enough to consult the gp. It would make sense to contact them again about stopping the medication so soon to lessen the chances of the infection becoming worse. I used to have steroid mouthwashes for oral lichen planus which were very similar in effect - metallic taste that lasted, but sometimes the decision is devil or deep blue sea.
Not sure you should stop steroids, you were given them for a good reason and presumably for a week or two - you need to speak to doctor if it's that bad.
Some on here have had same reaction, but they are on Pred long-term for their illnesses, not short-term acute occurrences like you.
"I was prescribed Cortisone for upper respiratory track infection on Tuesday.
... I stopped taking the medication immediately "
I trust that was AFTER speaking to your doctor? There is a lot of talk about self-medication being bad but self-stopping prescribed meds is equally as bad. They were prescribed for a reason - to prevent things getting worse and, potentially, you becoming sick enough to need hospital.
Most medications have some unpleasant side effects but sometimes needs must.
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