I need some advice on my weight routine. I do weights six times a week, that is, 3 upper 3 lower. I do three sets of generally 15 reps for each exercise.

For my upper body I do:
Chest: Barbell Bench Press
Back: One-Arm Dumbell Row
Shoulders: Arnold Press
Biceps: Seated Dumbell Curls
Triceps: Cable Pushdowns

Lower Body:
Quads: Wall Squats
Glutes: Gluteal Squeezes
Groin: Lying Abduction
Calves: One-Leg Standing Calf Raises
Hamstrings: Lying Leg Curls
Abs: Hanging Knee Raises

I am 15 years old and am wondering if these exercises are safe for me to be doing as I DO NOT want to cause injury to myself as my soccer season has started up. I do have some back issues (mainly upper back) and am not particularly flexible. I do not get pain with any of these exercises except in Arnold Press my clavicles pop in and out as I move my arms up and down. Is this bad? Should I change to another shoulder exercise because I have heard that Arnold Press is terribly bad for the rotator cuff.

Also, any other advice on better exercises for different parts of the body would be much appreciated.

IMO 6x a wk is to much,change to a fullbody 3x a wk using nearly all compounds.

You might want to do dumbbell shoulder presses instead of arnold presses until your shoulder gets stronger. Also, doing some rotator cuff work will be good. Try a side-lying external rotation with a light dumbbell.

Your routine is missing dead-lifts. This exercise is critical in building a strong body. Also, your not doing any vertical pull exercise like pullups.

Because your into soccer, you might want to look into unilateral exercises like single-leg squats and lunges to help prevent injury.

I don't really have time to be doing three full body sessions a week as I have school and soccer training so my afternoons are pretty full most days. I will do normal shoulder press from now on and replace squats with lunges. I am certainly not doing deadlifts as the last time I tried that I got a hamstring injury. I've heard you should only do it if you have a strong back and flexible hamstrings, and that I have neither. I will also do some rotator cuff work. External Rotation I have done before and was very effective.

How can you have time for 6 workouts a week but not 3?
You realise the full body workouts will consist of heavy compounds so as to take less time then you're splits which have too much volume and lack some key movements? (i.e. real squats, deads, pullups)
I suggest you read the Weight training 101 sticky

Squats are an incredibly effective exercise, you don't want to cut them out completely. So, alternate by doing squats one day and lunges the next day you would normally do squats.

How are you going to develop a strong lower back without dead-lifts? Try them using a light weight so you get used to the movement and learn proper form. Do a search on youtube for proper form deadlift, there are a few good videos.

In regards to your schedule - is it that you have time during the day, just not enough time to do a FBW? In that case, try a push/pull split - all your pushing exercises (squat, bench press, shoulder press) one day, then your pull exercises (deadlift, row, pullups) the next. Add in the isolation exercises as you see necessary. You could do this 4 days a week and see some decent results. You said that soccer season is starting, so I imagine that you have soccer practice a few days a week. In that case, you might not want to lift 6 days a week in addition to soccer practice as that might be too much. An important part of building muscle is allowing your body to rest and rebuild.

if you totally refuse to do deadlifts at least add in full extension planks with weight, and make sure your doing them properly, I went on vacation for a month last summer and couldnt do deadlifts, but i did planks and had my friend put weight on my lower back, when I returned to doin deadlifts i was actually able to increase weight so I guess they helped, i still think that deadlifts are irreplacable though and definitely dont get rid of the squats. If it were up to me I would get in lower body/back (core) in with compounds over anything else if I didnt have the time.