How would I get a roster of my unit during the Gulf War?

Did you try TogetherWeServed? There is also Military.com. Both are contingent on self election.

If the unit still exists, you could try to contact the unit's public affairs office. The PA office can help you get in touch with the unit historian (some poor guy's additional duty). He or she can look up unit history that may include a roster.

If the unit is closed. You may need to try the Navy History Office.

Look up units on Facebook. There are a lot of military groups