You do not give both at the same time. The antibiotic will bind with the vitamins in the chickens system, and be flushed out. You give one or the other. Ife chicken is presenting really really ill I treat with antibiotics first, then offer the electrolyte/vitamin solution once done medicating...
Is that the same tetracycline? I give that and then a vitamin/electrolyte solution, but not at the same time. The tetracycline will bind with the vitamins and be flushed from the system. I also use an infrared light and isolation if needed. It sounds like you're doing all the right things...