To Sue Or Not To Sue (insurance Is Claiming "no Fault" For $2000+ Damages)

Location: Pittsburgh, PA

Situation: Allowed car to be used to transport mutual friend (+kids) home. Approaching a "T" intersection with only right hand turns allowed in left lane. Car in opposing traffic turns too sharp and sideswipes my car causing damages to the fender, bumper, wheel+rims, and brackets totaling in estimate (from the opposing parties insurance) as over $2000.
I received call as the individual who was driving my car and the opposing party were pulled off into a parking lot exchanging information explaining what happens but i can hear the opposing party in the background apologizing profusely. Call cuts out before I can say to call police and get a record of the report (Their phone died) by the time I am able to reach them again they have already parted ways and no police were called. (Dumb. I know)

Insurances reach out to take statements and explicitly refuse to take a statement from the passenger who was in my vehicle. I filed a claim night-of and heard from the opposing parties insurance that no claim was made on her side for 3 days (had to do call backs through those days to get the estimate and such). It is now filed as a "word-vs-word" case as there was no other evidence available. (No police report or cameras at that intersection either)

It's a notorious intersection for people taking left hand turns too tight when coming from the direction of the opposing party. And from what I can find of my own research even with non-OEM parts the repairs would likely cost at least what the estimate that was provided

SO...

Question: Should I attempt to sue for damages and would I get the use of the passengers testimony to aid in that? Or would his testimony in the court of law be the same result as the insurance companies where its "non-impartial testimony" that wouldn't be considered as "enough" to help me?