Well, I'm no expert...didn't even stay at a Holiday Inn Express last night.
But, you really don't have much of a problem at all. If you're anywhere within 80-90% of your "package" speed rating, you're doing fine. The 3Mbps is the line cap speed, and a few factors such as protocol overhead and some other things take up some of that speed. So, your posted test of 2821 is right in there.
The about "May need help" part is a bit misleading for you. Verizon is now selling FiberOptic service to residential customers, so your speed is thrown-in and compared with those who have 10Mbps packages and such, so you can see why a 3Mbps connection would fall into a lower range compared to the top packages. Again, no problem.
My advice? Have fun with it!!!
-Matt