Daughter keeps scratching her eye

My daughter has been sucking on her hands a lot due to teething recently. But sometimes she misses her mouth and hit her eye and she’ll dig it. She got a cut there from it but she keeps re cutting it back open. She’s only 4 months old.

I always keep her nails trimmed but she just keeps ripping the scab off. I feel bad to put mittens on her since she sucks her hands for relief and comfort. Due to health reasons, she can’t hold pacifiers in her mouth and she hasn’t reached the point where she can hold stuff in her hands to put in her mouth, like teethers.

What can I do for the scab?