Can Tinea, eczema or drematitis spread to the eyes through contact lenses? Which part of it?

I have history of skin problem. It kind of Tinea, Ecezma or drematitis ( m not sure what it called ). It happens about 12years ago on my right hand since I was 11years old or s.th. When I wash clothes, or dishes, it will come. It was itchy, little rashes (with fluid in it), and my skin peels off. Sometimes come and sometime gone. When I use some Cotrimazole cream on It, it become better or gone. Till now, it come sometime, but not much like before since I stop washing clothes or clean dish. Sometimes, skin around my fingers are peels off.

I start using contact lenses for 4-5years already and never have any problem. But, 2months ago, I started eyestrain since I use iPad a lot, sleep less, look at closer items for long time, drink 4glasses of coffee every day with less water consumption and always stay in front of fan. So I visited Dr, and my eyes back to ok. He told I can use contact lenses sometime as I need.

During that time I use lubricate tears that'd gave me and use contact lenses once a week. These 3 I start having eyelids inflamed 2days after my 2nd day of wearing contact lenses. So, I visited another Dr. Gave me some medicines. 1eyedrops said for inflammation treatment, but long term use can cause fungus illness to eye or corneal. I used it for 1week already. Today, I visited him and he just check my eyelids and told me that my eyelids are almost fine now. So, I need to use it more, if better no need to visit him again.
Added (1). He said sometimes contact lenses solution can cause problem to eyes, but if I want to use it on next 2week is ok. I really need to use contact lenses since I have myopia. He told me to use eyedrops till my eyes are fine, but m not sure when. That eyedrops also can cause corneal and sclear thinner. Morever, I still worry even now my hands are fine, but skin problem can related to fungus. So, how long after stop using that eyedrops are fine before start using my contact lenses?

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