If you want real-time visual feedback from you voice you can use a tuning application. However the human voice is always in motion and very rarely matches the pitch perfectly. I've tried to sing while watching a strobe tuner application I have and I can tell you that vibrato makes this almost useless.
IMHO you would be better to try as has been suggested using melodyne or v-vocal to at least get a visual of what you just sang and use that feedback to correct the problem notes. Then if you want you can make the corrections in melodyne or v-vocal and listen to how it sounds. Then practice singing along with the corrected vocals.
You can use this same procedure practicing singing arpeggios or scales or whatever you like.
Remember it's not your eyes that need training it's you ears.