Ask relatives who don't live with you if they smell anything coming from you. Make sure you sit close to them and cross your legs and everything. Friends and especially people that live with you may have gotten used to it (and friends can lie to keep from hurting your feelings). But realitives tend to be honest (usually brutally). If people you don't live with don't smell anything, then you either only smell at random intervals (odd), or you have social anxiety disorder. I have this to a small degree myself. I am fine when I am with someone I know and pretty okay in places that I am used to, but to go to a strange new public place by myself makes me paranoid. For me, it's people laughing. I start checking my shoes for toilet paper and pull my shirt down and check to make sure my skirt isn't stuck up in my panties, wipe my mouth and nose, that sort of thing. It's quite possible that you are sensititve to people coughing and you check your smell like I check my shoes and clothes. Putting on cologne, bathing more, etc. won't help because you'll still be paranoid, even though you know you can't possibly stink. Me, I know I am dressed neatly and can't possibly be humorous, but I still check and double check myself anyways. If everyone agrees that you don't smell, believe them. There are medicines that can help you cope with the anxiety. I went to an all girls' university, so I can't say anything about the classroom grooming habits of young men, but the girls were all the time pulling out scented lotion and putting it on before class. It had nothing to do with anyone smelling bad adn everythind to do with dry hands, lack of time to groom before class, a need to show off some new beauty product, boredom habit, addiction to lotion, etc.
Here's a little secret that women keep to themselves (and I'm probably breaking some unwritten rule telling you this) but their underwear gets smells in it. That's because we have extra parts and we excrete extra stuff and a slight odor happens. However, dirty underwear isn't supposed to smell clean, so this is no big deal for you or for women. The rule of thumb in determining if your underwear is getting offensive is to smell the crotch of your pants. There should only be the slightest trace of scent there or none at all after wearing them all day. If your pants don't stink, then don't sweat the underwear odor; it's staying self-contained. Obviously wear a fresh pair everyday, don't wear the same pair of pants two days in a row (if they're not dirty and don't smell, then you can wear them multiple times before washing, but give them a day to completely air out before wearing again), make sure you wipe real well after BMs and when you're not in public, you should wipe after peeing too to keep down odors, and, if it will make you feel better, put a cup or so of baking soda in your bath. That kills odors and the bacteria that cause them (and makes your skin soft).