Is tobradex (tobramycin and dexamethasone) effective for eye dryiness problems?

No. I don't recommend using an antibiotic-steroid preparation for dry eyes. The potential side effects of allergy, cataract, and elevated intraocular pressure are enough concern. More appropriate dry eye treatments: artificial tears, gels & ointments are effective. Warm compresses & lid massages, humidification of living environment; punctal plugs, restasis; fish oil infrequently--mild steroid.