Brief Answer:
Most probably a boil

Detailed Answer:

Hello,

Swelling in right armpit with redness can most probably be due to a boil. This is being a common site for such thing as there is more sweating that is retained here.
Redness is due to inflammation or infection.
It is better to do the following in such a situation:
Clean the area with plain water.
Apply Liquid Povidone Iodine.
If the swelling is not subsiding it is better to take an anti-inflammatory like Ibuprofen if it suits you. And an antibiotic to control infection.
Another cause like an inflamed lymph node must be ruled out.
I hope you do not have diabetes and there is no lump on the breast area or any focus of infection in the right upper limb or breast area.

You may please photos if possible.
Please give feedback.

Hope I have answered your query.
Let me know if I can assist you further.

With Regards.

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