Back up photos from Nexus 5 do not appear on Google +

First off, I am technologically "challenged", so I usually have trouble performing the most basic tasks on phones/computers, etc. Recently my phone battery has been dying way too fast and for no apparent reason. Yesterday, the phone had no power although it had been plugged in all night and it repeatedly turned itself off when I tried to engage it. I left it plugged in all day and tried again last night. Nothing. I panicked and found some advice online. Finally got it going again. I thought I had better back up my photos (around 1,500) to Google+ before I lose the phone forever. I followed instructions and a small window on the phone said the pictures were being loaded. I kept the external power going. The battery did come back to about 85%. Then I left the phone and my Mac on all night. This morning, it (the phone) said there were 650 pictures remaining but I had run out of space. I then paid for the basic ($1.99/month) space and hoped that the rest would be uploaded. So far NO pictures have appeared on Google+--I have looked everywhere. I don't know what to do now. I am leaving the phone turned on and connected to external power since I'm afraid what will happen if I turn it off. (Right now the battery seems to be at about 10%!!) I hope someone out there can help me before I lose all my pictures which are really important to me. Thank you.