iPhone SE - force rebooting gets into a loop
I don't think this is related to plugging into the rental car.  

I also have (had) an iPhone SE and it experienced the exact same problems.  I took it in and was told the sleep/wake button on top was bad.  The repair place told me they don't bother repairing these models anymore because the parts are very hard to find; this model has a bad problem with this type of button failure.  If you google it you'll see. 

I ended-up going to Best Buy and they recycled it for free.  I think you're out of luck unless you can find a place to repair it.