Can ear inf cause tight neck muscles?

No, but....: If you have tight neck muscles you may also have tight jaw muscles. In the case of tight jaw muscles you can have pain around the jaw joint. Pain around the jaw joint can seem like "ear pain ". Many times people who have jaw joint pain think they have an ear infection and I have seen many patients with jaw pain misdiagnosed as having an "ear infection.".

Yes: If the infection leads to lymph node involvement in the neck region it can make the neck feel stiff as if the muscles are tightening due to there increased size and inflammation.