Guidance needed

Greetings. My 2012 195k mile V which has driven flawlessly to date yesterday had a concerning problem and seeking some guidance. I drove around 30miles to a friends farm. Last mile is a sandy dirt road, if that has any chance of being an issue, where I drove around 20mph. Anyway after my visit I start the car and it sounds terrible like something in the in the timing chain/belt area was really loose, and apparently my friend who was behind the car said it was smoking. I turned it off after 5-6s of that. Waited another min or so, and restarted. It made a noise for a second and then smoothed out. I drove very gently around 20miles back towards home and it felt normal. Made a quick stop but kept the car on while I ran in the store. Get back in the car and as I turn onto the street and give some throttle it lurched twice somewhat violently even under the ~20% throttle I gave it. Drove as easily I could to get back home, which I thankfully reached without any additional drama.
Any thoughts on what this is? Oddly I never got a check engine light. I will however try to see if any minor codes are in it when I scan it later today.
Thank you for your help.

 

Checked and the coolant is normal level and no creamy oil cap. So first win.

 

Is it normal just after sitting 45min after running fine before that for a 40-45mile trip? Since it was a ‘start’, but not really a ‘cold start’. Thanks