Can my infected ear piercing cause the lymph nodes behind by ear to be tender?

Yes, very likely: Any infection of the skin can cause the regional lymph nodes to enlarge and become tender. It means you need to take antibiotics for which you should go see your doctor and let him/her examine you and assess the seriousness of this infection and treat it appropriately.

Reactive Lymph Nodes: Yes. The posterior auricular nodes drain the ear and posterior scalp. I would expect them to react if you underwent an ear piercing complicated by infection. Please monitor the infection carefully. The bacteria that cause skin infections can include resistant organisms like MRSA. An antibiotic resistant organism in your head and neck region could be life threatening. Are you on antibiotics?