Will using a higher octane damage my engine?

That’s what I’ve been doing. It’s an automatic transmission (I think you’re under the impression its a manual), so when I have it in drive the transmission likes to stay in high gear and the torque converter coupled even when I’m trying to go uphill or get up to speed. For instance, I could be accelerating at 30-35 mph uphill and instead downshifting into 3rd gear, the transmission stays in 4th and chugs along at 1000 RPMs, thus the pinging occurs.

I’m not a leadfoot so I’m trying not to floor the accelerator…instead, I’ll change the gear selector to 3rd or 2nd gear to keep the engine spinning faster for the extra torque and smoother acceleration (which stops the pinging).