I was the same way when I was young and now, at over 50 my wife is very proud that I get erect just from touching her with clothes on.
I would think that if the woman suspects that you have a erection this would be a good thing. Her pussy will get wet and she will want you even more. Tell her that she is making you hot. She will know what you mean.
You don’t run away from women with erect nipple’s?!
My suggestion is to develop outward self confidence. Also masturbate the day before and the day of your encounter. There are also de-sensitizers on the market. I’m sure this will work-out.
You could also watch more porn.