I requested quota increase on the YouTube API though the google developer console from 10k to 100k.
I received a successful email, that says my increase has been approved
However if i check the UI in Google developer console it still states my quota is 10,000 per day.
When will my quota increase take effect?
The first thing i would do would be check that you are looking at the correct project. As this quota will be only valid for the project you applied for.
Then you need to edit the quota and increase it yourself. You should have that option to do that now. If you don't have that option I would wait a couple of days, to see if it doesn't kick in.
You might want to start sending requests and see if the quota increase is actually there its not not appearing in the UI yet.