Don't want to lose weight but want to lose fat?

I'm a naturally petite person, I weigh 100lb and I don't need to lose weight but I feel "skinny fat". I'm wanting to lose my tummy pooch and tone up my arms and thighs. Any tips? I am starting to exercise but I don't know where to start, or what I should be eating. I'm breastfeeding too so I can't cut calories.

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