World doesn't appear in singleplayer screen

I had been on version 16w02a and my world would appear and load and everything was fine. I copied that world as a back up and put it on my desktop before entering the version 16w03a. When 16w03a loaded up I went into singleplayer and realised that the world didn't appear as an option to play. So I thought oh well, i'll just go back to 16w02a and play it. But when I did so the world still wouldn't appear. So I thought lucky I had a backup, but after switching the backup world in even 16w02a wouldn't load it. I have no idea what to do, I'd been working on this world for a long while.

I got the launcher info up and this is what it said
Completely ignored arguments: [--nativeLauncherVersion, 286]
[16:56:14] [Client thread/INFO]: Setting user: DivinePixel
[16:56:14] [Client thread/INFO]: (Session ID is token:9affafecb344433a974506c069071b9e:746719e7e391412f8babb811e218a1c8)
[16:56:15] [Client thread/INFO]: LWJGL Version: 2.9.4
[16:56:17] [Client thread/INFO]: Reloading ResourceManager: Default, Edited Pack, Star Wars
[16:56:21] [Client thread/ERROR]: Realms module missing
[16:57:17] [Client thread/ERROR]: Exception reading C:\Users\lukes\AppData\Roaming\.minecraft\saves\Creaters World\level.dat
e: Loading NBT data
at dx.a(SourceFile:123) ~[16w02a.jar:?]
at dx.a(SourceFile:82) ~[16w02a.jar:?]
at dx.a(SourceFile:26) ~[16w02a.jar:?]
at azd.a(SourceFile:82) [16w02a.jar:?]
at azd.c(SourceFile:66) [16w02a.jar:?]
at aza.b(SourceFile:57) [16w02a.jar:?]
at bhl.e(SourceFile:35) [16w02a.jar:?]
at bhl.<init>(SourceFile:28) [16w02a.jar:?]
at bhj.b(SourceFile:43) [16w02a.jar:?]
at bey.a(SourceFile:367) [16w02a.jar:?]
at bcc.a(SourceFile:881) [16w02a.jar:?]
at bff.a(SourceFile:237) [16w02a.jar:?]
at bey.a(SourceFile:341) [16w02a.jar:?]
at bff.a(SourceFile:498) [16w02a.jar:?]
at bey.k(SourceFile:404) [16w02a.jar:?]
at bey.p(SourceFile:381) [16w02a.jar:?]
at bcc.s(SourceFile:1563) [16w02a.jar:?]
at bcc.au(SourceFile:949) [16w02a.jar:?]
at bcc.a(SourceFile:390) [16w02a.jar:?]
at net.minecraft.client.main.Main.main(SourceFile:122) [16w02a.jar:?]
Caused by: java.io.EOFException: Unexpected end of ZLIB input stream
at java.util.zip.InflaterInputStream.fill(InflaterInputStream.java:240) ~[?:1.8.0_25]
at java.util.zip.InflaterInputStream.read(InflaterInputStream.java:158) ~[?:1.8.0_25]
at java.util.zip.GZIPInputStream.read(GZIPInputStream.java:117) ~[?:1.8.0_25]
at java.io.BufferedInputStream.read1(BufferedInputStream.java:284) ~[?:1.8.0_25]
at java.io.BufferedInputStream.read(BufferedInputStream.java:345) ~[?:1.8.0_25]
at java.io.DataInputStream.readFully(DataInputStream.java:195) ~[?:1.8.0_25]
at java.io.DataInputStream.readUTF(DataInputStream.java:609) ~[?:1.8.0_25]
at java.io.DataInputStream.readUTF(DataInputStream.java:564) ~[?:1.8.0_25]
at dn.b(SourceFile:407) ~[16w02a.jar:?]
at dn.a(SourceFile:68) ~[16w02a.jar:?]
at dx.a(SourceFile:117) ~[16w02a.jar:?]
... 19 more
[16:57:17] [Client thread/ERROR]: Exception reading C:\Users\lukes\AppData\Roaming\.minecraft\saves\Creaters World\level.dat_old
e: Loading NBT data
at dx.a(SourceFile:123) ~[16w02a.jar:?]
at dx.a(SourceFile:82) ~[16w02a.jar:?]
at dx.a(SourceFile:26) ~[16w02a.jar:?]
at azd.a(SourceFile:82) [16w02a.jar:?]
at azd.c(SourceFile:74) [16w02a.jar:?]
at aza.b(SourceFile:57) [16w02a.jar:?]
at bhl.e(SourceFile:35) [16w02a.jar:?]
at bhl.<init>(SourceFile:28) [16w02a.jar:?]
at bhj.b(SourceFile:43) [16w02a.jar:?]
at bey.a(SourceFile:367) [16w02a.jar:?]
at bcc.a(SourceFile:881) [16w02a.jar:?]
at bff.a(SourceFile:237) [16w02a.jar:?]
at bey.a(SourceFile:341) [16w02a.jar:?]
at bff.a(SourceFile:498) [16w02a.jar:?]
at bey.k(SourceFile:404) [16w02a.jar:?]
at bey.p(SourceFile:381) [16w02a.jar:?]
at bcc.s(SourceFile:1563) [16w02a.jar:?]
at bcc.au(SourceFile:949) [16w02a.jar:?]
at bcc.a(SourceFile:390) [16w02a.jar:?]
at net.minecraft.client.main.Main.main(SourceFile:122) [16w02a.jar:?]
Caused by: java.io.EOFException: Unexpected end of ZLIB input stream
at java.util.zip.InflaterInputStream.fill(InflaterInputStream.java:240) ~[?:1.8.0_25]
at java.util.zip.InflaterInputStream.read(InflaterInputStream.java:158) ~[?:1.8.0_25]
at java.util.zip.GZIPInputStream.read(GZIPInputStream.java:117) ~[?:1.8.0_25]
at java.io.BufferedInputStream.read1(BufferedInputStream.java:284) ~[?:1.8.0_25]
at java.io.BufferedInputStream.read(BufferedInputStream.java:345) ~[?:1.8.0_25]
at java.io.DataInputStream.readFully(DataInputStream.java:195) ~[?:1.8.0_25]
at java.io.DataInputStream.readUTF(DataInputStream.java:609) ~[?:1.8.0_25]
at java.io.DataInputStream.readUTF(DataInputStream.java:564) ~[?:1.8.0_25]
at dn.b(SourceFile:407) ~[16w02a.jar:?]
at dn.a(SourceFile:68) ~[16w02a.jar:?]
at dx.a(SourceFile:117) ~[16w02a.jar:?]
... 19 more