Can ear infection leave damage in future? like headed dizziness.

Maybe: There are three types of ear infections: outer ear - "swimmer's ear" - usually painful - not associated with dizziness; middle ear infection - typical infection that children get - usually painful - unlikely to cause any residual dizziness; inner ear infection - usually viral and not painful - may leave residual dizziness.

Some basics: The era prior to antibiotics taught us a lot about middle ear infections. We know even bacterial infections would usually self heal over several months. Some with chronic infections would have the sensitive ear bones frozen in muck leaving chronic hearing loss. Occasionally the infection would erode into the skull & need surgical drainage. Viral infections of the inner ear can produce vertigo.