Here is a link to an old MedHelp thread about your concern. I hope you can find something useful in it to help you.
If not, please don't hesitate to get back with us. We'll all do our best to come up with some ideas for you. Here's the link and best of luck!
http://www.medhelp.org/posts/Anxiety/Aniexty-and-body-odor/show/5052
Peace
Greenlydia
And know that the above poster wrote one sentence that REALLY hit the nail on the head!
I have never heard of anxiety causing body odor, although this may be my ignorance. Have you addressed the anxiety to determine if this is what is causing to feel you have an odor? If not, then it's time you do, you may be surprised! If you bathe regularly and use deodorant, and have good oral hygiene, you shouldn't have body odor. There are reasons for bad breath, but you don't mention it being your breath as being the problem.
I think if you had body odor your family would notice, you spend a lot of time with them in close quarters. Check out the anxiety as the problem, you have nothing to lose and everything to gain. You need to address every possible reason for this. Good luck and take care.