How to proxy outgoing TCP/UDP requests and/or mask the source IP

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http://serverfault.com – My web-app tracks various online services and to do so, makes frequent outgoing TCP and UDP requests (through PHP). Unfortunately, my web-app was recently hit by a DDoS attack. To counter it, I installed a proxy for incoming requests (CloudFlare) and this seems to work well. However, due to the outgoing requests my web-app makes, the attacker was able to trace the source IP of my webserver and attack it directly, completely bypassing the incoming proxy. I need a way to hide my IP from outgoing requests, possibly by proxying requests via node machines or something. (HowTos)