Do I qualify for Operation Inherent Resolve Ribbon?

It’s a pretty simple answer. Did you physically spend time in Iraq or Syria? Was the time long enough to qualify for the award (30 days consecutively, 60 days otherwise if I remember correctly)?

If the answer to either of these is no, then you don’t rate.

IAW AR 600-8-22 CH. 2-19 I do not believe so.
From the Reg:
Individuals authorized the IRCM must have served in direct support of Operation INHERENT RESOLVE (OIR). The AOE encompasses the land area of the countries of Iraq and Syria, the contiguous waters of each extending out to 12 nautical miles and the air space above the land area and contiguous waters. The IRCM period of eligibility is on or after 15 June 2014 and before a terminal date to be prescribed by the SECDEF, under regulations to be prescribed by the SECDEF, or under regulation to be prescribed by the Secretary of Transportation with respect to the Coast Guard when it is not operating as a service in the Navy.
c. Servicemembers must have been assigned, attached, or mobilized for 30 days (consecutive or nonconsecutive) to a unit operating in the AOE