Generally, they do not use antibiotics for a month. What is usually done is being given two different kinds of antibiotics for about two weeks. At the same time, some sort of acid reducer is given, perhaps a PPI.
Although stress can cause stomach upset, it is unrelated to h.pylori. Also, not all individuals who are infected with h.pylori develop ulcers, but immediate treatment is necessary. Your doctor can always run tests to see how much damage has been done to your stomach. If you have, in fact, had h.pylori for some time, it could have caused gastritis and/or peptic ulcer disease. Stomach cancer is really only a factor if left untreated.
H.pylori can be contagious, afterall it is a bacterial infection. Make sure that you and your family wash their hands, eat food that has been properly prepared, drink safe water. Although they are unsure of its definate cause, they do believe that it derives from "bad" food and water intake.
Good luck... and don't worry... worrying only makes things worse. :-)
E.
p.s. You may not even develop a yeast infection, not everyone does.
p.p.s. Your dad is in our prayers.