By upgrade I meant upgrading to VPS if you'd like to remain with the same host.
But as I never faced that problem (maybe because my site's just 2 months old and I don't have traffic), so I think you can think of moving to a new host.
if you'd like suggestions about new hosts, I highly recommend you spending a day at
www.webhostingtalk.com, you can get the best solutions there regarding hosting.
my sites are hosted at
www.netwayweb.net and till date, I am highly satisfied with them. *crossed fingers*