Help is here

Hello there, I am  Platinum level Zerg.  Every single Zerg player has gone through what you're going through, and there are ways to stop these cheeses.

To stop that Terran Triple Barracks (Which is what they're doing from you're description) Simply keep an eye between 2-3 minutes and see if the Terran is fast expanding or not.  If you do not see a fast expansion, sac an overlord is around 5 mins.At this point you will see his barracks, a factory making hellions, or maybe even a Starport preparing for banshees.  If you see just barracks and he's not expanding, he's pretty much just handed you the game.  I don't know what your opening build is, but I go 14 Pool 16 Hatch, as soon as my hatch is down I get one gas geyser, get Ling speed ASAP, then throw down a Baneling nest, by the time he attacks you can have a lot of speedlings with some banelings, then it comes down to micro to stop the attack.  After it fails you can do a baneling bust, or macro up and easily win with whatever composition you want.
To stop a 4 gate is very similar, open 14 Pool 16 Hatch, if u see 1 pylon 1 gateway and a cyber core building as his first three buildings, he is doing 4 gate almost certainly, especially in Silver League.  How to respond is simple, get gas after you put your hatch down, get ling speed and build 2-3 spines at your natural.  Once you begin researching ling speed you can pull 1 or 2 drones out of gas because you won't need gas for a while.  AT this point just mass as many lings as you can, if you want to keep getting gas and get the carapace or melee upgrade that's ok.  Mass lings, and wait until he attacks.  Make sure you only engage when your spine crawlers are attacking as well.  Also keep and overlord at his natural, if he expands, drone up on your two bases and do a 2 base attack asap with preferably ling/roach.  If he doesn't expand just wait until he attacks and crush him, then macro up or attack with lings and win.
Hope this helps :)