Canon 70-300mm blurry wide open at infinity - stars and distant lights

I believe what you are experiencing is the result of one or more issues.

First, I would say that tails are indicative of trailing which is caused by the speed setting. Depending on your focal length, speed affects the shot differently. 10s on a short focal length won't produce long trails as it can on a long focal length. The way to mitigate this is following the rule of 500 that can help determine the maximum speed you should use when shooting at a given focal length. Note that you stated your camera is a Canon T1i, that is a APSC crop factor of 1.6., while a full frame would be crop factor 1.

Second, the teardrop nature makes me think this can be a result of coma, where stars in the corners appear tear drop, but point towards the center. This seems to be caused by the nature of most lens optics being curved. The other common possibility is a problem with collimation, where the lens elements are not aligned well, but I don't think that is happening here.

This video on youtube appears to be using a similar lens to yours, and it also seems to suffer from teardrop stars - this makes me think that it is not a collimation problem with your lens and instead is the lens element curvature causing coma. In the comments of another video by the same creator, he attributes the problem to coma. He seems to try to manage it by shooting an area, and then trying to crop out the sides with more severe teardrop stars.

This may not be the best lens for astrophotography. If you delve more into astrophotography, I recommend the dpreview astrophotography forum section for some discussion on technique and lens/telescope selections. They may be some astrophotography subreddits as well that can offer discussion on this.