Phthalates are related to vinyl/plastic items or those coated with those materials. Fabrics are phthalate-free, as long as they are of the usual fibers like cotton, wool, polyester, etc. Unless your items are in a few specific categories of feeding/sleeping items, this won't be a problem.
Fabrics are also on the exempt list for lead content, as they inherently do not contain significant lead. Printing on them, vinyl appliques applied, metallic threads in them or waterproofing would all make them no-longer-exempt from lead content testing or documentation.
But you will need to label correctly for both CPSIA requiremtns and the FTC care and content requirements.