Signed both Form 1040-NREZ and Form 8843. Will it be a problem?

No, I would not expect that to be a problem.  While I understand that Form 8843 says to sign only if filing on its own, this is likely to inform people that are filing it that it needs to be signed.  As long as you signed your Form 1040 (or Form 1040NR-EZ), you should be okay.

But in Form 8843, it says "Sign only if filed by itself". But i filed both Form 1040-NREZ and Form 8843

Please see the updated answer.  I would not expect that to be a problem.  It is likely instructed that way to inform people that it does NEED to be signed if filing on its own.