Plz, can we use tobradex (tobramycin and dexamethasone) for children?

Not a good idea. If you are thinking of using leftover med for your kid, it is not a good idea. If your kid has pinkeye, I would at least consult with his/her doc. Instillation of this steroid/abx drop in some cases can allow a viral infection by the herpes virus to cause long term damage.
Yes, . The dex part of tobradex (tobramycin and dexamethasone) , is a steroid. Tobradex (tobramycin and dexamethasone) is not indicated for bacterial infection.