I put my contacts in when I have a cut on my finger?

I feel like one of my lenses may have come into contact with it, please reassure me that I won't somehow get an eye infection or something? I got the cut several days ago and have washed my hands loads, and did just before I put my contacts in - but I haven't used any alcohol or anything on it.

I thought there was just one but there seems to have been a bit of cut on the skin above it too (no red blood marks on this smaller cut, it looks like I just split the skin a bit)

Should I take my contacts out immediately or is any damage that may happened already been done? How soon will I know if something's wrong? And can I still wear contacts tomorrow?

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