My mom used to use Sea Breeze when I was a kid, and I remember how much it made my eyes water because of its overpowering scent. It also made my face burn when I used- kind of akin to putting rubbing alcohol on your face.
I recently purchased a bottle of Sea Breeze Sensitive Skin, now 15 years after using my Mom's Sea Breeze. My, how things have changed! The scent is now nice and light- no more teary eyes, and it is very mild- no burning skin. I usually use this once before bedtime, after I have already washed with a facial cleanser.
I think this is somewhat inconvenient to use, because it comes in a liquid, so you have to buy cotton balls to apply it to your face- it can be a little messy if you soak the cotton ball too much; a little goes a long way. That being said, it really does work well- even after cleaning, the Sea Breeze removes even more dirt and make-up from my face that was left by my soap. I use the Sea Breeze on my neck too, which makes me feel nice and cleaned up before heading to sleep.
I would give this a try!