Where can I drill my ears or nose in chengdu ?
Do you mean pierce your ear or nose?
If you head towards the Northern part of the city, there are tons of tattoo shops that probably do piercings as well.
Please note that Hepatitus is rampant in China and I highly doubt that many of the tattoo places sterilize their equipment, at least to the same level as reputable places in the west.
You could also go to Huaxi hospital and ask around.
You may just want to play it safe and do something like this in your home country....
There is a shop on Yulin Nan lu between 2nd ring road and Fangcaojie, I think it's called fishbone, been there for a decade or so and has some reputation.
The advice about going to the northern part of the city (do you mean around the North Railway Station) seems just silly and not safe...
Majority of good (clean, safe) tattoo shops will pierce your ears, it's much more difficult to find a place where they pierce nose...but for example here http://weibo.com/u/2109646102 you can have it done