Could my mom be sick with the same symptoms that i had 3, or 4 weeks ago when i was sick with my sore throat, coughing, gagging, huh? just wondering.

Possibly: Such events are possible, as throat infections are often contagious. Throat symptoms can be from a strep throat infection (antibiotics are needed), a cold virus, influenza (Tamiflu may be needed), or from some other cause such as allergies or irritants. Usually, a person sees the doctor if the sore throat is bothersome, is with moderate or high fever, or with much coughing or worrisome symptoms.

Maybe/not: Three to four weeks is a bit long to incubate either strep, flu or any other germ you may have carried. If you passed it to her it would likely happen within days to a week.