When adding a contact, I cannot save their phone number under the catogory of iphone. Only the "mobile" option shows up, where as before I had a "iphone" option. I want the iphone option so I can imessage long distance without a charge.
The label you assign to a number in the Contacts app doesn't have any effect on the amount you are charged. I believe the way it works is when you add a phone number, Apple checks it against their own records and if they find that number there (and you can contact Apple's servers at the time you try to send) then it will send text messages through the iMessage service rather than through the regular phone network.
That aside, I'm not sure why the iPhone label wouldn't appear unless it is already in use for another number for that Contact. Each label can only be assigned to one number per contact.
When you add or edit a contact on an IOS device there is an option to select or add a custom label.
When you tap the green "+" to add a contact (for example) the label is underlined. It's a hyperlink/button, tap it. the "Label" screen will slide up. You can then select from a list of labels and if you scroll past the preexisting labels there is an option to "Add Custom Label."
"iPhone" is a preexisting label on my iPhone (IOS 8.4) but if it is missing you should be able to add it as a custom label.