It wouldn't be share 'with', because that would be used for only two people (I shared my sandwiches with my sister). I would say 'between the three of us'. 'Among' or 'amongst' would be possible if it were something that could be split up and 'shared out' (eg money, food). I don't think 'among' would work in the situation of using a towel.

I believe the correct preposition would be amongst .