Can I check my density altitude with brake tension?
You may be able to get a rough estimate of if your engine is producing sufficient thrust utilizing brake pressure. But, how will you determine how much thrust is being produced? Your brakes are not calibrated so carefully as to adequately determine that. You would only be guessing. You might get a better indication of engine performance by utilizing the sound of the engine.
The best way to tell if your engine is producing enough power with a fixed pitch prop is using your tachometer. One is required for all flight in a powered civil aircraft with a standard category U.S. airworthiness certificate in the US by 14 CFR 91.205. With a constant speed prop, you are required to have a manifold pressure gauge to indicate the power output of the engine.
On the other hand, even if you could judge your engine output without instruments, it still would not account for the effect of density altitude on the lift producing airfoils. Instead, you are better off determining density altitude using the weather data that you should have reviewed during your preflight planning required by 14 CFR 91.103. For that, you need no aircraft instruments.