The mobile interface is a cut-down feature set of the full site, intended for quick-browsing, asking and answering. As editing your profile isn't something that is done often, it is likely that it was deliberately left out of the mobile site as the majority of users wouldn't be using this functionality on a day-to-day basis.
If you absolutely need to update it now and no PC/tablet is available, depending on your mobile browser, You could set it to display in desktop mode and edit your profile from there, and switch back when you're done.