FIG. 1 is a front perspective view of a cosmetic carrying case showing my new design;

FIG. 2 is a front elevational view thereof;

FIG. 3 is a rear elevational view thereof;

FIG. 4 is a left side elevational view thereof;

FIG. 5 is a right side elevational view thereof;

FIG. 6 is a top plan view thereof;

FIG. 7 is a bottom plan view thereof;

FIG. 8 is a front perspective view of a modified form of a cosmetic carrying case showing by new design;

FIG. 9 is a front elevational view of FIG. 8;

FIG. 10 is a rear elevational view of FIG. 8;

FIG. 11 is a left side elevational view of FIG. 8;

FIG. 12 is a right side elevational view of FIG. 8;

FIG. 13 is a top plan view of FIG. 8; and,

FIG. 14 is a bottom plan view of FIG. 8.

The broken line showing of a closure element in FIGS. 1-14 is for illustrative purposes and forms no part of the claimed design.