Hi and Welcome to HealingWell, Onikaze!
Those are great questions! First of all, whenever you body is fighting an infection it usually causes a fever, which in most cases is good, as that means your body is fighting the infection off!
Sometimes Dr.'s do treat allergies with fever with antibiotics as a preventive to a secondary infection. As an example, you may be prone to getting sinusititis with your allergies, so they give the antibiotics to help prevent this from happening.
Re low grade normal temps. I have that problem, too. :) However, you are not considered running a temperature unless it's one degree more than 98.6.
As far as exercising with a fever goes, that's something that I'd prefer you ask your Dr. individually, as I don't know all your other health problems.
As a general rule, when your body is fighting an infection, you do not want to add more stress to it than it's already going through, but again, this is something to discuss with your Dr.
Wishing You Well!! - It was nice meeting you, come back soon!