safari history not showing on iPhone

1. First off, check to make sure you are actually viewing the History list (as opposed to the Reading List or Shared Links). Simple i know, but a common cause of this issue. Assuming you are looking in the correct location:
2. Try a reset: Simultaneously hold down the Home and On buttons until the device shuts down. Ignore the off slider if it appears. Once shut down is complete, if it doesn't restart on it own, turn the device back on using the On button. In some cases it also helps to double click the Home button and close all apps BEFORE doing the reset.

Hmmm. Try this:

Settings app > Safari

1. Change the current Search Engine (you can change it back later)
2. Turn ON Search Engine Suggestion and Spotlight Suggestions
3. Tap Clear History and Website Data
4. Reset the device as stated above.

I don't think so, at least not based on what you have posted thus far.

You can try turning Private Browsing on, then off again. But other than that I'm out of suggestions.