The key to surviving a massive influx in traffic is to increase the amount of concurrent requests you can handle, that means a)decrease the time it takes to render pages so you can serve more visitors quickly, or b)get a hosting platform that is capable of handling more connections.
If you expect lots of media traffic, shared hosting is not for you. At the least you should temporarily upgrade to a VPS or dedicated server - this is a critical time for your business (and you) and you don't want website and email trouble.
If you're short on time, I wouldn't recommend moving to something like cloud - you're not going to be horizontally scaling much as far as know (but I've almost no experience on that - I might be wrong). You'd also potentially have to go through changing DNS and changing hosts - which can be a traumatic experience depending on support teams on both sides. See if godaddy can you up to a dedicated server - this would provide you dedicated CPU time and ram and get you out of an environment where you're potentially going to be shut off for affecting other users. You might only be on this plan for a month or two - then you can make a decision if moving back to shared hosting is right for you.
If you have time to move a copy of your site to a dedicated server before re-pointing the DNS, you should see if you can benchmark that copy of your site before it goes live to see if you need further optimization or if throwing cash at it was enough. You can with something like apache ab if you have access to a linux machine (or can grab a cheap linux vps) - a quick guide on this can be found here:
As to other optimizations, SQL server is probably faster than access, and could probably be setup on your dedicated machine or a VPS. You'll want to get the site developers involved and see if they can implement any caching or if they can make any database optimizations, as those will lower the time it takes to render a page and move onto the next visitor.