I think Kagome gets upset at InuYasha's comment because, to her, it implies that he thinks she's somehow unaffected, or has overcome her pain. But she hasn't. She's still hurting. And while InuYasha recognizes—and even apologizes for overlooking—Kagome's pain after the fight with Kaō, I don't think he really understands the source or the severity of that pain. Kagome intentionally shields him from the former (when she keeps Kaō from saying who is hurting her), but I think she wants InuYasha to understand the latter, at least to some degree.
Strength can often be a burden. "You're so strong" suggests that the other person does not see—and thus cannot ever help you with—your own struggles. Kagome's outburst is her immediate gut-wrench reaction of, "This isn't easy for me, I'm still feeling and struggling with this, please see that."