Iphone 5s not adding in new contacts to phone?

I have the Iphone 5s, when I add new contacts they are not apperaing in my contacts list. I have synced all the contacts in the settings, I have unsycned and resycenced from icloud already. The strange thing is when I go to text messages and type the name it appears right away but when I look for the same indiviudal in my contacts it is not there.

Not sure

Try resetting the phone

Try adding in your contacts manually one by one instead of syncing them. It might take a long time but that may be the only way