Problem using internet browsers after upgrade to High Sierra

I can't help with Chrome but here are some suggestions for Safari:

Force Quit Safari ( command + option + esc keys). Then restart Safari holding the Shift key.

Turn off Safari extensions in Safari > Preferences > Extensions > un-checkmark all extensions.

Empty Caches. You can either choose Safari menu > Clear History Or, if you do not want to remove History go to Safari menu > Preferences > Advanced and check the “Show Develop Menu” in Menubar. Then, on that menu > “Empty Caches”.

See these Apple Support Topics for detailed advice:

If Safari is slow, stops responding, quits unexpectedly, or has other issues - Apple Support

If Safari doesn't load a page or webpage items are missing - Apple Support

Safari for Mac: If Safari can’t open a website

Start by going to System Preferences->Network.

Do you see a green ball next to Wifi?

What do you have for "Configure IPv4": in most cases it would "DHCP".

What is the first number in your IP address? Something starting with 192 or 10 is the most common.

If all that looks normal, the most likely cause is a DNS or proxy issue.

Click Advanced..., then DNS. What do you see under the DNS servers? One or more addresses starting with 192 or 10? Or something else?

Also, click on Proxies. Usually under "Select a protocol to configure", none of the boxes should be checked.