Hello luvdance24,
I am sorry to hear that you are unable to get your photos off of your iPhone because it is not responding. I can understand the importance of getting your photos, so let's see if we can get them off your iPhone.
I first want to point out that if your iPhone is not responsive then you will not be able to get your photos off. Now if it is unresponsive, you can try to restart your iPhone by holding the Sleep/wake and home buttons for about 10 seconds or until the Apple logo shows up. If that works for you and can access your home screen, then you should be able to import your photos to your computer or make a back up to iCloud or iTunes. Take a look at the articles below for more details.
Restart your iPhone, iPad, or iPod touch
https://support.apple.com/en-us/HT201559
Import photos and videos from your iPhone, iPad, or iPod touch to your Mac or Windows PC
https://support.apple.com/en-us/HT201302
How to back up your devices using iCloud or iTunes
https://support.apple.com/en-us/HT203977
Let me know if the helps or need further assistance on this issue.
Take care