try to soft reset it. (hold home button+sleep button at the same time until you see the apple logo) If you changed the screen yourself, did you disconnect the battery while removing the screen?
Had a customer with this problem on the S6. I had to take off the back panel and remove the buttons and clean them. Set them back in and they were fine.
Take out your sim card, connect to wifi. Wait for the phone to be connected to wifi then set in your sim card. If the sim card has a lock code on it, unlock it. If it's saying no service after that then it could be something wrong with your sim card. Try another sim card if you can.
alot of times the red screen or blue screen is a result of damage to the screws in the con shield over the lcd cables(screws set in the wrong place or direct damage to the logic board in the screw hole) or your camera flex cable is broken. at least in my experience
I use a chinese supplier also, and never once have they asked us to send money via western union. We always pay directly online, have been using them for quite a while now. they also have a buy back program where you can ship your broken glass (lcd still works) and they will fix the glass and send it back to you for a very low price. http://www.ettrends.com/ They are really safe and their customer service is great. (english is very broken though :P )
Had the same problem, we changed our first 6s screen (a phone we bought cheap with a broken screen) we bought some 3rd party screens with the lcd attached and the 3d touch would work on the left side of the screen but not the right. We bought this phone just to try.. conclusion.. don't buy 3rd party screens.. take it to apple.. Not until the distributors can master the 3D touch at least.
as long as you dont have any 3rd party parts on it, they should accept it under warranty. Apple is well aware of how bad the iPhone 6 frame is.. Considering they have made the 6s much stronger. I had a customer with the same problem and had a warranty.. Instead of taking his money to fix it. which i easily could have.. i directed him to the local apple shop. 2 weeks later he came back to let me know that apple replaced his phone