Great description with your question!
Most homes are on cable and the more your neighborhood uses it, the more you will see spikes in your internet. FIOS is about the only way to avoid the spikes.
Speedtest was a great idea and you did not say if 11Mbps was correct for your contract. I use Netflix and play WoW. In my experiance, 30 Mbps is acceptable (baseline) for MMO's and also Netflix. The lag (latency) you see when playing (you hit the NPC and it dies 30 seconds later) is you game sending data and getting the data much later than you should. Usually this is result of your bandwith, which at 11 Mbps, isnt a lot.
If your speedtest is correct, then you can tweak your NIC some to improve performance.
First, make sure your NIC driver is current by going to the Control Panel, Device Manager, select your NIC, properties. Note the name of the NIC, who made it and the published date of the driver. Then go to the NIC manufacture's website and look for a newer driver. You may need help in installing them if you find newer ones.
Once you have checked the NIC driver, you can reset the settings on how Windows uses the NIC to default. This will correct any previous tweaks your network stack has had and ensure that any changes going foward are what you want. To do this Microsoft has an Fixit tool. Look up Microsoft Document 299357 and use the fixit tool.
Then there is a utility to optimize the OS / NIC settings for MMO games. The most recommened utility is Leatrix Latency Fix 3.0.
Go to www.leatrix.com and download version 3. Unzip the package and run the exe. This utility is designed to tweak you NIC to reduce Lag.
Note - there are many websites deboted to this subject. So look around and be comfortable with this step.
For your computer, download Malwarebytes, install it, update it and run a full scan. Your symptoms dont sound like malware but its worth being sure.
Ultimately, your TV and Netflix is the most honest indicator. If Netflix is buffering, you likely dont have enough bandwidth. Your TV isnt subject to all of the stuff you and I have written. If Netflix isnt doing well, you need more Bandwidth. Contact your ISP and talk about The Speedtest results.
Good Luck