Styes are caused by Staphylococcus which is a contagious bacteria so that by touching your originally infected eye to your other eye you transferred the bacteria to the other eye. Avoid touching the stye.
Use a cotton tipped applicator to apply medication. I recommend that you telephone your doctor and have him order erythromycin opthalmic ointment and apply it according to the directions on the tube.
In the meantime, take Motrin according to the package directions to relieve the pain and swelling of the stye and also place crushed ice in a baggy and apply the crushed ice on your stye for 20 minutes an hour until the swelling and pain subsides.
Hot compresses will cause the stye to become more painful and swell much more so I recommend you reduce the swelling by applying ice and taking Motrin. The infection will be eliminated in a few days after being absorbed and eliminated through your circulation.