Frequent, tiny cold sores

I've been getting these really small, single-blister cold sores around my mouth for about a month. I've been on antibiotics for the past 10 days and just finished the course for strep and a sinus infection caused by a weakened immune system from a REALLY bad sunburn. I don't feel like my immune system has really bounced back, but I've been getting the cold sores for about a solid month now. Every few days another one pops up. They never reached the blister stage until I got two brand new ones on the actual skin of my lips (it's like a mirror image, one on each side) instead of the regular around the lips. My usual regimen is lysine lip balm which has worked fantastically, rubbing alcohol to dry the blisters, and Releev which is a new thing for me but I'm not really impressed by it.
I'm getting really sick and tired of constant cold sores, I'm about to start my period and i'm getting really depressed from these stupid cold sores, which only causes more.
I really need help.