The ornamental design for a portablehangingtower for medical use, as shown and described.
FIG. 1 is a front perspective view showing my new design;
FIG. 2 is a front view of FIG. 1;
FIG. 3 is a rear view thereof;
FIG. 4 is a left side view thereof;
FIG. 5 is a right side view thereof;
FIG. 6 is a top view thereof; and,
FIG. 7 is a bottom view thereof.
The broken lines showing the remainder of the portable hanging tower for medical use are directed to environment and are for illustrative purposes only. None of the broken lines form a part of the claimed design.