When changing the rear taillight bulb, now the right blinker doesn't work and niether tallight work. I changed left and right bulbs

Beth your central problem goes back many years. for some reason bulb makers thought it would be funny if two electrically different bulbs physically fit into the same socket. those where the 1156 and 1157 bulbs. if you have ever driven down the road following someone who had one very bright tail light and one dim one, then you have seen this at work. When the round sockets turned into flat blade sockets this nonsense was continued. what you have done there is inadvertently put the wrong bulb into the wrong socket. half the guys working in repair shops and all the guys working in gas stations and all boyfriends and husbands, except me, are unaware of this and make the same mistake. if you have a 50/50 chance to get it right, the odds are against you.

You need to do some thinking about what the socket is for, are there two functions going on such as a tail light and a brake light, and which bulb then goes into which socket. there will be two more or less the same in appearance on either side. a dealer cam most likely set you straight on this for free.