Why does my DD214 not reflect that I was deployed in support of Desert Storm in 1999?

1999 wasn't Desert Storm. It was Operation Southern Watch.

From AR 600-8-22

2–14. Southwest Asia Service Medal
a. The SWASM was established by EO 12754, 12 March 1991, as amended by EO 12790, 3 March 1992. It is
awarded to all Servicemembers of the Armed Forces of the United States serving in SWA and contiguous waters or
airspace there over, on or after 2 August 1990 to 30 November 1995. SWA and contiguous waters, as used herein, is
defined as an area which includes the Persian Gulf, Red Sea, Gulf of Oman, Gulf of Aden, that portion of the Arabian
Sea that lies north of 10 degrees north latitude and west of 68 degrees east longitude, as well as the total land areas of
Iraq, Kuwait, Saudi Arabia, Oman, Bahrain, Qatar, and United Arab Emirates.
b. Servicemembers of the Armed Forces of the United States serving in Israel, Egypt, Turkey, Syria, and Jordan
(including the airspace and territorial waters) between 17 January 1991 and 30 November 1995, will also be eligible
for this award. Servicemembers serving in these countries must have been under the command and control of the U.S.
Central Command or directly supporting military operations in the combat theater.
c. To be eligible, a Servicemember must meet one or more of the following criteria:
(1) Be attached to or regularly serving for 1 or more days with an organization participating in ground or shore
(military) operations.
(2) Be attached to or regularly serving for 1 or more days aboard a U.S. naval vessel directly supporting military
operations.
(3) Be actually participating as a crewmember in one or more aerial flights directly supporting military operations in
the areas designated above.
(4) Be serving on TDY for 30 consecutive days or 60 nonconsecutive days. These time limitations may be waived
for people participating in actual combat operations.
d. The SWASM may be awarded posthumously to any person who lost his or her life while, or as a direct result of,
participating in Operation DESERT SHIELD or Operation DESERT STORM without regard to the length of such
service, if otherwise eligible.
e. One bronze service star will be worn on the suspension and service ribbon of the SWASM for participation in
each designated campaign (see para 6–8 for further information on the bronze service star). (The designated campaigns
for SWA are listed in app B.)
f. See AR 672–20 for the Civilian Service in SWASM.

Didn't ODS/DS end in 91?