Yes it is, very contagious! I have the same herpes simplex and managed to get a cold-sore on my eyeball about 15 years ago, which had me in agony for 4 months, staying out of bright light as eye would water, not focus properly due to sore in front of pupil, and had to stay away from school and not share anything. Pillows had to be changed every day after sleep and I was not allowed to stroke any pets. If I touched my eye, I had to wash my hands before and after. Treatment might be better now, but I had to have numerous drops/dyes in it, but mine was an extreme case. I have scar tissue (microscopic) on my lens which can only be removed by laser treatment. I did manage to get prescribed Zovirax for free for 5 years though, which was the only bonus. If you want any more info, let me know as I remember everything as if it were yesterday!