That it suddenly got better, as this test I just did shows:
http://www.webpagetest.org/result/131220_77_1FV/
Means the host dealt with the real problem site that was slowing down the server. It's not you.
These dishonest companies over sell their shared hosting on purpose, then give you the upsell schtick when you have trouble. This is why i am saying get a responsible host not a upseller ripoff specialist.