I tried removing the battery but that didn't work, and tried holding the power button-volume button and that failed also. But, thanks to the comments regarding the volume button, I finally figured out what may be the problem. I have a cover on the phone that fits very tightly, and I wondered if it was pressing on the volume button to the extent that it was actually triggering it. So, I took the cover off, rebooted the the phone, and the Safe Mode was off.
Thank you all so much!