It should be fine to use antibacterial and antifungal nail drops together. However, anti-fungal nail drops are not a very effective treatment for nail fungal infection.
A nail fungal infection, also know as onychomycosis, is often difficult to clear with just using topical anti-fungal creams or drops. This is because penetration of the cream or drops into the nail is poor.
Topical amolrofine nail lacquer can be used to treat milder and more superficial fungal nail infections.
In more severe cases, oral systemic anti-fungal treatments may be required but these can cause side effects such as liver toxicity. Treated is usually for 3 to 6 months.
It is good to confirm a diagnosis of fungal nail infection with a fungal smear or culture before starting on the anti-fungal therapy.