How can I find out what my unit awards are? Is there a website to find it or any other way to find out?

Ahh, the Choctaw code talkers. Lot of history in the 142d Infantry Regiment.

HRC maintains a .pdf* that contains all published General Orders in one document, so you can easily search for the unit awards (make sure you read the first few pages - it will make your life easier).

A quick search showed an AUSA and a MUC.

If you're really interested in digging deep, you can go the the U.S. Army Center of Military History* and search for your unit.
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* https://www.hrc.army.mil/wcmt-api/sites/default/wcmtfiles/files/16333_0.pdf
* USACMH - https://www.history.army.mil/html/forcestruc/orghist.html

My first reaction was surprise that a unit would have any doubt about the unit lineage and honors, then I started checking the usual sources and found that the 142nd Infantry seems to have about disappeared in current official history, at least online.

The Texas Military Forces Museum's "Lineage and Honors" page for the unit doesn't mention any unit awards.
https://www.texasmilitaryforcesmuseum.org/36division/archives/142/142lin.htm

The US Army Center of Military History lineage and honors page for Infantry Regiments jumps from the 137th to the 148th without any mention of the 142nd.

The Institute of Heraldry (TIOH) used to maintain files with the lineage and honors of each unit, but that function appears to have been transferred to the Center of Military History. TIOH still has files on the distinctive unit insignia, but I'm sure you have that already.

It looks like you really are going to need to search through the entire General Orders file or your unit can formally ask the Center of Military History for more information.

Here are some resources for finding unit awards for the National Guard:
HRC website
Scroll down to Promotion Evals and Awards, then Awards and Decorations, and then Unit Awards
Center of Military History (CMH)
Verify what a unit has listed on their official Lineage and Honors
National Personnel Records Center (NPRC)
Authorized requesters can request copies of documents from military personnel records online
DOD 1348.33-M
Consult this document from September 1996 for a listing of all approved JMUAs