when i initially replied to your post i assumed you may be more in the beginning stages of lifting, assuming makes an ass out of u and me, mainly me. i still stand firm on saying no isolation work, splitting your legs into different groups and hitting them in iso exercises isn't going to do shit for strength or size, and won't help your squat at all. all those muscles need to work together to do what they were built to do. just like you'd see better progress benching heavy once a week rather than hitting triceps, chest and shoulders seperately with extensions, flies and raises respectively. so with that being said, if it hurts to throw a 315 pound bar on your back but doesn't to do so with 225, then i would take this time to do a back squat cycle. squat three times a week, you're accomplishing multiple things when doing this. giving the injured muscle a break and shifting focus to something else you may not have focused on before. practicing the movement. have a light day, medium day and a heavy day, with the heavy day of course being as heavy as you can go without hurting yourself, not hurting yourself to go heavy. this is going to get those muscles really used to working together to accomplish this task, prime your central nervouse system for lifting heavier weights, and burning the motion into your muscle memory. practice makes perfect, and strength is a skill. so for your light day you could do 60% of your 1rm. (note: when i say your 1rm, let's take 90% of your true 1rm and call that your 1rm, as to not agitate your trap. so we're talking 60% of 90% of your 1rm on light days. for example if your true 1rm is 315, then 90% of that is 283.5, so let's round down to 280. 60% of that is 168, which is actually only 52% of your true 1rm. but we want to work in common percentages here like 60, 80, 85, 90, so that's why we do this. also your true 1rm is when form really breaks down, so when you hit your *new* 1rm, you're still keeping proper form). so do 60% for 10 sets of 3. do body weight glute ham raises and body weight calve raises. hit any upper body exercises you feel like on this day to maintain your other lifts. medium day is 80% for 5 sets of 3, romanian deadlifts, 1 upper body lift. heavy day is 90% for three doubles with weighted standing barbell calve raises, body weight glute ham raises or weighted for less reps if you can, and your upper body exercise. also something i just thought of is can you do front squats without hurting your trap? with a clean hold racked position, not arms crossed. if so can you hit your 1rm for front squats without irritating your trap? i say this because at one point my back squat was weak and form sucked. so i made the decision to do strictly front squats, for a long time. i did them for 3 months or so, maybe longer. not one back squat. it is MUCH easier to keep proper form with no one watching you when doing front squats, you also will naturally go deeper. it will also take SOME compressive force off your back, but your back still has to stabilize, it puts a greater emphasis on your abdominal muscles and obliques. one day after about 3 months front squats and no back squats, and very minimal leg press (did them from time to time for fun), i hit a pretty good new personal record for a 1rm. at this point i thought, what the hell let's throw this on my back and give it a whirl. i missed back squats. (btw this new 1rm for front squats was more than i had ever back squatted, but don't get me wrong front squats are gonna be way weaker than back squats when starting out). i repped this weight out on highb ar back squats after using ito to set a new 1rm for front squats after my legs were smoked already. that's how much strictly front squatting correctly improved my back squat after 3 months. coincidentally this is probably about how long it will take your trap to heal if rested properly. i've made the switch back to back squat and have never been stronger. my mobility is improved, i'm squatting ass to calves what i never could have dreamed of lifting to just parallel. my form is almost impeccable, and because my back squat is shooting up so much it is affecting my deadlift, which is shooting up right along side with it. so if you can front squat heavy as hell without hurting your trap, then i sugest that. front squat heavy once a week, other days when working on upper body which ever way you can, throw in your assistance lifts for the front squat. do your gluteham raises or rdls, hip thrusts, box jumps, sled pulls, etc. good luck.
