Brief Answer:
you should be examined by your doctor

Detailed Answer:
Hello,

your doctor can determine whether this is an infection (which is the most likely cause) or not. If it's an infection, it's important to know whether it's probably caused by bacteria or viruses. Viral illness cannot be treated and you only have to wait until it gets better by itself. Bacterial illness can (and should) be treated to avoid complications for you and to decrease the likelihood of spreading the infection to your baby. If - for example - it's a streptococcus then treatment with penicillin will almost 100% decrease the transmission rate after the first 24 hours of treatment. Besides that, streptococcal pharyngitis in a baby may cause various serious complications like rheumatoid fever, kidney disease, etc, so you'd better not take the chance.

Gargling and other local measures do not reduce infectivity and they certainly do not speed up the recovery process.

So in conclusion, it's very important for a breast-feeding woman to receive appropriate treatment in time, so a visit to your doctor is absolutely necessary.

I hope you find my comments helpful!
You can contact me again, if you'd like any clarification or further information.

Kind Regards!

---