Yes, some cell phone use/distracted driving is allowed for adults in most states[0], but most states do not allow 'young drivers' to use a cell phone at all[1]; and texting is specifically banned or partially banned for all drivers in all but two states (Montana and Arizona)[2].

[0]http://www.iihs.org/iihs/topics/laws/cellphonelaws/maphandhe...

[1]http://www.iihs.org/iihs/topics/laws/cellphonelaws/mapyoungc...

[2]http://www.iihs.org/iihs/topics/laws/cellphonelaws/maptextin...