I swear though. These clichés have kinda started to bug me. I've never known anyone to pant or get super sweaty from catching a cold or a fever.
Even when I was on meds that weakened my immune system and I came down with a fever that was a little higher I wasn't panting or sweaty. I just felt noticeably warmer and tired than usual.
Don't get me wrong, I totally understand that manga isn't meant to be realistic and these are just clichés to bring the two love interests closer but still.
Different symptoms for different people I suppose, not to mention that there's also an age factor to it: nowadays when I get sick I barely notice it, going on through my day as normal, but apparently back when I was but a tot I came down with a fever so big that I wavered between consciousness and unconsciousness, with a temperature so high that my parents thought I was going to die (may have been parent panic but they tell me I have never gotten as ill as that one time ever since).
So yeah, with fever being the body's method to protect itself by raising its own temperature, I'd say it's perfectly possible for someone, specially one fully clothed and inside a warm bed, to sweat their life out IF their own inmune system and viral reaction isn't as strong or prepared as other people's.
Also, remember that japanese people have a culture that puts greater emphasis on being clean than ours (public bathing and hot springs for example), so their standard of being filthy is far higher than ours.