HT3529 Contacts not found in contact list after saving from new text message

Question

When a new number texts me and I save it to my contacts, I can find that contact when texting, but contact does not show up on my phone list contacts.  For Example: I received a text message from [phone].  I  #1 clicked "Contact" in the top right corner of the text message screen, #2 clicked "i" button, #3 clicked "Create New Contact," #4 added first and last name, and #5 clicked "Done." 
In the future, if I try and text that saved number, the contact will appear under the saved name.  But if i press the phone icon and look at my contact list, the contact is not there.  So if I try and text "Heather Campbell" i can find the contact by clicking new message and typing "Hea" and send her a text message with no problem.  However if I go to my phone contact list and try to call her, she is not listed as a contact.
Please Help!

Answer 1

Unfortunetly, that's not the problem.  I have 3 groups.  1. All iCloud  2. All Hotmail  3.  All Facebook.  I have the All iCloud checked, i do not want facebook friends and email addresses in this contact list.  This will only give me a list of phone numbers I saved from call log.  Not phone numbers I saved through text message.  Thank you though!