TvZ

As a high gold Terran, how do I deal with Zerg when they go roaches + speed lings and keep me stuck on two/three base? I've been having major trouble in this matchup, because when this happens my drops get shut down by queens and lings, I can't seem to move out without getting massacred by just massive amounts of roaches, and if I do get a nice composition and move out I find out the Zerg has infestors and is extremely close to getting either ultras or brood lords, and I don't have the tech required for either and I just... die. 

This applies especially to meching, since that's a strategy that I've been trying to work on and really big roach play has just been killing me. 

Help, fellow Day9 viewers? :D