You don't have to ask for or even accept pity. The point is to take ownership of the situation. People closest to you grow accustomed to your stutter and have an unspoken understanding, but it's still reassuring to both parties if you acknowledge that you stutter sometimes and appreciate the patience. Make it just a candid reflection instead of "addressing a problem." It's okay that you stutter and it's okay that your brother's GF stutters. If you can internalize that, the embarrassment will go away.