Until you're using what you already have to full potential, upgrading your gear won't improve your results unless you also upgrade your knowledge, skill, technique, and experience.
The rest of this answer will be dedicated to shooting still images as the video part is expressly off topic here. Keep in mind that the 7D does not have the capability of continuous AF while shooting video, so the answer for video use will be totally different. You'd be much better off asking about shooting video in this situation at video.stackexchange.com.
The entire development of autofocus technology over the past 30+ years has been driven by the desire to apply it to shooting sports and action with more accuracy and consistency. Sure, it's nice for other applications, but the cutting edge of AF technology has always been about sports/action. That's where the gains have first been made that then can also be applied to other forms of photography.
If you're going to shoot sports or action in a low light environment the usual approach is to use the widest aperture that gives acceptable image quality. This allows one to shoot at lower ISO than would be the case using a very narrow aperture. The noise reduction needed when shooting in a dim environment at very high ISO, such as ISO 6400 with the APS-C Canon 7D, will reduce image detail to the point that the entire image will look blurry anyway, even when shot at f/11. Also keep in mind that for full resolution still images shot with the 7D, the diffraction limited aperture (DLA) for the 7D is at f/6.9. By f/11 one will likely be able to begin to see the detail reducing effects of diffraction even when viewing the image at less than 100%.
The 7D has a very configurable AF system. It does take some work and practice to learn how to use it to its full potential. Like any complex tool, the more options it gives the user the more skill the user needs to use those options to their advantage. It's not the most consistent AF system in terms of accuracy from frame-to-frame but it does do well enough that many photographers have managed to get some good action shots with it.
Canon EOS 7D + EF 70-200mm f/2.8 L IS II, ISO 2500, f/2.8, 1/400 sec.
Canon EOS 7D + EF 770-200mm f/2.8 L IS II, ISO 1600, f/2.8, 1/200 sec.
If the 85mm focal length gives you the field of view you desire, then consider an AF lens such as the EF 85mm f/1.8. It's a fairly popular 'budget' lens for shooting indoor sports. Use it at f/2.2-2.8 with whatever shutter speed you can get away with based on your subject's movement and set the ISO at what you need to get decent enough exposure. Depending on your post-shooting workflow, you can leverage the power of raw image processing to use shorter shutter times than would otherwise be the case.
For further reading:
When should I upgrade my camera body?
Should I upgrade my Canon body or lens for upcoming travel?
After 2 years of amateur photo, buy a new body or a great lens?
Which lens for portraits using an APS-C camera?
Should I upgrade my body or lens first?
Choosing between Lenses Canon 70-200 f2.8L IS II vs Canon EF 70-300mm f/4-5.6L IS USM
Should I buy a new DSLR or spend the money on a photography course with my point & shoot?
What is better than a Canon d1100 but still affordable? (The accepted answer to this one includes plenty of links to other related questions here that may be helpful to understanding how the photographer is the main contributor to the quality of an image while also acknowledging that sometimes a piece of gear may be part of the problem.)
Can great photographs be taken with not-so-good equipment?
Will a better lens help with high speed skateboarding shots?
Why are my photos not crisp?
How do I diagnose the source of blurry photos?
I'm having trouble getting sharp pictures while shooting a concert from a press pass location
This answer includes a large number of links, grouped by the primary cause, to other questions here that address various issues that affect image sharpness.
Lots of noise in my hockey pictures. What am I doing wrong?
Blown out blue/red light making photos look out of focus
Or you could go ahead and totally switch systems because you're using the wrong lens in the wrong way for what you're trying to shoot.