Creating a new contact in contact list but it doesn't show I've found lately that whenever I add a new contact it then doesn't show in my contact list either in the app or the phone. If I receive a call from them their name shows and if I want to send a message I can type in their name but I can't search for them if I want to call them for the first time. 

I haven't changed any settings in my phone and wonder how to make this change.
Sounds like an issue with contact groups.  There are two places to check.

First from a contacts list screen click "Groups" in the top left and see if you have any contact groups that are unchecked.  

Second go to Settings > Contacts and see what default account is set.  This effects what group is used when creating new contacts.