It appears that either your connection to YouTube is being throttled in some way or it's a congested server.
As YouTube uses a different codec in Chrome than Firefox, I would suggest testing Firefox (or Internet Explorer) with a few HD videos. Chrome uses the VP9 codec, where as Internet Explorer and Firefox both use the H264 codec, so YouTube will likely fetch the videos off a different server.
Another possibility is HTTPS based connections being throttled. One simple test to check is download a large file from a HTTPS connection see what throughput you get. One example is the standalone Chrome browser package which is served from a HTTPS connection:
https://www.google.com/chrome/browser/desktop/index.html?standalone=1
Based on your above speed test, you should get a similar speed to what I got:
If this downloads very slowly at the time YouTube is having trouble playing in HD, then it's very likely HTTPS based traffic is being throttled on your ISP. Otherwise, if you're just having trouble playing YouTube in HD, it's possible YouTube is trying to play from a congested server or along a congested path to it.