Ok, that's different than what I was thinking before.
First, did you delete hosting on http://www.upstatepridesc.org/ at dreamhost? Then you would enter the CNAME record. Then you have to WAIT for DNS propagation. That usually takes about 12-24 hours for most of the USA, but could take up to 3 days to reach all nameservers worldwide. This isn't a function that dreamhost controls, its a fact of life and the way DNS works.
Since I'm seeing a dreamhost "bad_http_conf" error on when I click http://www.upstatepridesc.org/ I suspect that you have not deleted "hosting" on the dreamhost side. But that's not conclusive since if I try to do an nslookup on www.upstatepridesc.org I see
which actually doesn't make sense, because I'm seeing your CNAME entry, plus the IP addresses which all resolve to: proxy.heroku.com which hasn't yet come up in the discussion, so I'm not certain how it is related.
Another option you have to change nameservers on the domain and let bellstrike manage the DNS. Is that an option via bellstrike?