?s on what may cause headgasket failure & what signs I may see if it's the issue

What is your question?

I just finished a thermostat swap & an extensive coolant flush due to some idiot adding wrong coolant in our car...Unfortunately this was right b4 a 2hr trip we'd be taking. w/our luck the symptoms of this stupid little mistake didn't show up until, you got it, 2hrs from our home. Financially we weren't able to afford towing it home that far nor did we want to wait til morning, & find a mechanic in a town we we're unfamiliar w/. So considering it was sundown in mid March(KS so just above freezing)we chose to limp it home 15-20miles at a time pullin off to cool down soon as the temp gauge read 3/4 so not quite to the point where our car dings to say warning over heating. In the now 10hr trip, unfortunately we heard the over heating ding 4-5 times due to road side pit-stop options. So My ?'s-could those few warning dings been enough heat to cause headgasket failure & if so what symptoms might I see? Would I see oil mixed w/ coolant or vice versa? How serious of issues might this lead to?

How long has your 2012 Dodge Avenger had this problem?

Couple months