For your example, you would actually use a dash, or double hyphen:

I kept my bag in my lap. It kept all my belongings including two pairs of clothes–-not including the ones I was wearing–-and my wallet with my I.D. and the money I had made previously.

I think there's actually an ALT code that you can use to make a dash (which is just basically a longer hyphen, just not called that) but I can't remember what it is and 99% of people just use double hyphens anyway.