When we are in trouble, let us not always forget to consult the logs, it has the hints to address the problem.
Squid, as far as I know, does not by default blocks http access unless you defined something to block certain sites or if your web app is connecting via a port like
and that port was not included in its default configurations of safely allowed ports.
acl Safe_port port PORT#
If you are also running another layer of proxy behind squid that handles application filtering like a content filter with file extensions blocking, this could cause your problem and you will need to consult its manual.
But if still your webapp is really in trouble when behind any http proxy, this suggestion is not practical considering and can only become your last option if only very few of your users needing frequent access to that webapp.
1. Add another NIC in your firewall box.
2. Don't bind squid on this NIC's IP. Assign to this your next network IP block.
3. Don't port forward outgoing http traffic from this network block to squid port.
4. Give this a separate switch/hub and therefore a separate network. This is almost like a DMZ.
5. If you have a good structured cabling installed with Patch panels, simply switch your clients' patch plugs to this switch/hub and this would force yo to separate your users accessing your webapp.
6. Configure your firewall if possible to allow specific traffic (ports & protocols) to traverse between your separated networks that are needed like SMB/Windows/Netbios and others.