Carbs are OK at certain times, but it's the timing that is most important. I used to think right after a workout was the best time, as some sports supplement manufacturers suggest, but it depends on your goal. Carbs have value during active competition, when muscle glycogen runs low and blood sugar levels need to be restored as soon as possible, say, during a marathon. The problem for you with carbs after your workout is two-fold: your body will not need to burn off stored fat, and the production of growth hormone will be curtailed as carbs are being metabolized.
From your original post it appears you want to burn fat and heal an old injury, so carbs would interfere with both after a workout. Quickly absorbed proteins, on the other hand, would insure the body does not need to cannibalize muscle in order to find an energy source in lieu of carbs. The closer to your workout, the more important these things are. The rest of the day and on non-workout days, low-glycemic (slower absorbed) carbs like whole oatmeal are a good way to restock your main energy source, that is until the last meal of the day, which should once again lean towards proteins and away from carbs and fats. The reasons are similar, because fats and carbs will interfere with your sleep and hormone production, while proteins will enhance this process, particularly for the sleep hormone melatonin.
You are wise to take care when selecting grain products. The endosperm of a plant is meant to provide the raw material for seed germination, and it is a very concentrated energy source that has an explosive effect on blood sugar levels when ground into flour and ingested in the form of breads, cakes, and processed cereals. Whole grains have to be broken down to release their carbs, therefor are lower-glycemic and less likely to trigger fat storage. They also take more energy to digest. It is easy to get too much of a good thing with grains, though, so restrict their use after lunch. Ditto for white potato products and white rice, while brown rice and sweet potatoes (ironically) are lower-glycemic.. if you've got to eat starches at all. Watch yourself closely, and you will see how many simple-carb choices we are faced with each day that are entirely unnecessary. Dressings, sauces, buns, pastas... the people who eat them usually grow fat. Eventually, when your metabolism has been restored, you will be able to eat some of these things without gaining weight, as I and many runners can now, but the change does not happen overnight.
It will, however, happen much faster if you follow the workout I suggested. The beauty of the short, intense workouts is that you will get the maximum 24-hr fat-burning benefit with minimum wear & tear, and maximum healing potential for your knee. While I wouldn't call these measured workouts sprints, they may seem that way at first. The idea is to finish the eighth repeat feeling like you could do one more just as fast. In other words, try to stay under control.
Regarding exercises for the quads, in many cases dysfunctional, unbalanced quads are behind knee pain, as I suspect may be true in your case after the accident trauma (see diagram from Gray's). A muscle is not a monolithic structure, and can be relaxed in some spots while being hypertonic (tight) in others. Your goal should be to find the tight spots and iron them out, without messing with the rest of the muscle. When you have restored the muscle to its normal, relaxed state, your knee pain should diminish and strengthening exercises will be productive. The exercises can make the muscle worse otherwise, which is why people often have to stop exercising to heal. You can't go wrong by relaxing the tight muscle first, before you begin retraining.
http://upload.wikimedia.org/wikipedia/commons/thumb/1/14/Rectus_femoris.png/250px-Rectus_femoris.png

The above rendering shows the area, just below the knee, where the muscles of the quad and Sartorius muscle insert and intersect. Of the five individual muscles at this junction (Vastus Intermedius not shown because it is under Rectus Femoris, the one most likely to produce pain under the knee is V. Medialis, on the right. The spot where the name tag is drawn should be your most productive spot to rub. You may want to check and see how this area feels when you attempt to sit "indian style," activating the Sartorius (far right), just to see if it is involved.
On running shoes, make sure any support shoe does not restrict your natural movement, or you may find as others on this forum have, that more things start to hurt that didn't hurt before you switched shoes. If you must err, err on the side of too little support rather than too much. A recommendation for control shoes is not a ringing endorsement of your running style, so there may be some biomechanical issues to address. Some stores offer running analysis, and I think you should find out what your style of running is, so you can make the necessary changes before something else begins to hurt. Changes may include a customized orthotic for your shoes, which when properly designed, can be more important than the shoe itself. This is more productive than trying to force yourself to run a particular way, because your running style tends to reflect the structure of your foot (which you can work with), as well as the knee and hip, which you can't do much about (you can do some things, but that's another story).