There is no need to test because of this encounter.
I would suggest get yourself tested for STD. It is a simple test and will make you worry free. Signs of STD take about 3-7 days to appear. Sometimes it can be asymptomatic. I would not rely on sanitary wipe handed over by any person. It depends on how careful they are , because they handle so many customers and a slip is possible now and then. So go to your physician and request an STD test. The earlier the better.
You should post your second question in Men's health or sexual health.
Is the redness on the meatus right after sex due to the flow of blood to that area?
You have to have direct sexual contact with another person who has an std to get an std.