Sounds like traffic is not being NATed or routed out of the Pi, so clients can talk to the LAN but not the internet.

Check by running in terminal:
sudo sysctl net.ipv4.ip_forward

If it returns 0 then thats your problem.

If so edit sysctl.conf and add:
net.ipv4.ip_forward=1

Then enable:
sudo sysctl -p

If that's not it then it is something in your iptables or allowed IPs on your client.