Non itchy red bumps that keep appearing?

[Aaron0794]

Recently I had itchy throat and sort of itching inside the nose. And doc diagnosed it as allergic rhinitis and prescribed some antibiotics as it had some infection,after that I felt  like my itchy throat is not going away, he prescribed some tablets for another 10days. And I have really bad headache sometimes. Been over two months now I have cough which looks non productive but some mucus is there though. Again on antibiotics.
And two-three weeks ago I started noticing some non itchy red rash on my knuckles and arms. Initially appear as flat then develop bumps, at times on my face too. But mostly on arms, it takes about a week to get completely faded away and then appear new one,  and this is painful when pressed.I have been stressed out about this for months now.

Is this non itchy red bumps (1-2mm in size) that keep appearing some sort of allergies??

The red tiny bumps mostly appear anywhere from fingers to shoulders on both arms (7-8 at times) . And sometimes on forehead too.

Do this rhinitis takes months to cure?