Here's a strange one. I have Yosemite 10.10.3 and no updates required but don't seem to have Photos app. Any suggestions as to how I might get it?
As Photos is supposed to be included in the 10.10.3 update automatically, I would suspect something may have gone wrong with the OS update itself.
In cases like this, I would always try downloading the current combo updater from Apple - currently 10.10.3 from https://support.apple.com/kb/DL1804 but you can always Google for "Apple combo updater [current number]" to find the latest.
The combo updater, unlike the regular delta updater, includes all changes since the last major update, in this case 10.10.0
I would also run Disk Utility & check permissions & drive integrity - before & after running the combo, just to be certain.