Would writing "caring solicitudes of empathy" be redundant?

Yes, "caring solicitudes of empathy" would be redundant. So would "empathetic solicitudes with care." The latter would also be incorrect in treating solicitude as a count noun. It's a mass noun, like empathy.

If you say the girl began with expressions of solicitude, that conveys "care" and "empathy" sufficiently that those words add nothing. Likewise, "expressions of empathy" would include the idea of care and solicitude. Care is a less precise term than solicitude or empathy, so one of the latter two words is preferable. Using both would be redundant, using all three doubly so.