I have a four year old female brindle with very bad breath and she scratches under her front arms a lot

I would say dental disease is why her breath is bad. That needs medical attention from a vet. Don't be shocked if teeth need to be pulled. Smelly breath typically indicates a rotten tooth.

Scratching in various places such as arm pits, ears and eyes, feet and flanks usually indicates an allergy. Finding out what can be costly and timely. The first thing I would change would be the food. Change to a grain free, hypo-allergenic food. Wash her in a shampoo that is specifically for itchy dogs and give her some diphenhydramine (benedryl). The dose for benedryl is 1mg per 1lb of body weight. So if your dog weighs 50lbs, you'd want to give her 50mg of benedyrl. If you purchase benedryl, ensure that it has no extra additives... just pure diphenhydramine.

Dogs get seasonal allergies just like people. If the benedryl isn't working for her, it's probably a food allergy. Food allergies take time. It takes approx. 6wks for a dog to adjust and/or react to a foods ingredience.

Will she let you look in her mouth? If so check her teeth, tartar can build up and cause bad breath and gingivitis. She could also have something lodged in her teeth or in the roof of her mouth causing the odor.
As far as the itching goes, inspect her for fleas, they tend to hang out around the warmer parts of the body and on the rump.
She could also be allergic to something causing the itch.
Could be that she has a skin infection in that area if the skin overlaps and stay moist.
I'm just guessing here, but if you check and find fleas then for the most part they are pretty easily controlled, given they are not infesting the environment.
It's worth a trip to the vet to get these checked, she is young still but dental cleanings are very beneficial to the health of your dog.