Let's take this one at a time...
Are the pictures you are trying to sync from the computer to your iPhone visible on the computer? Under Window File Manager or Finder (Mac)?
What computer do you have, a Mac or a PC?
If a PC, is it Windows 10 by any chance? Issues with iTunes there....
If PC, what AntiVirus are you running? McAfee or Norton? If so shut them down temporarily. Make sure Real Time/Protection is OFF for now and then try iTunes again.
As a simple step to try first please do the following. Hold down the Home and Wake/Sleep buttons at the same time for about 15-20 seconds until the Apple logo appears. Ignore the "Slide to power off" text if it comes up. You will not lose anything.
BTW, unrelated to you, I may or may not be able to respond for a while. I and others have been having issues accessing new posts on the ASC website. I have reported this to the moderators who told me that they are working on the issue, that it is affecting many, but they do not have an ETA for a fix. This has been going on for 2 days now.