I'm 45 years old and just started running last summer to measure my fitness using the Marine Corps Physical Fitness
(pull-ups, 2-minute sit-ups, 3-mile run). I am not built for running (big hips, short legs, hyper-extended knees), but I can now run 3 miles in 23:35. Here is what I learned that may help you:
1) Warm Up
You're a young guy, so you may feel you can just hit the ground running. But pains in your body could be the result of not warming up. The best warm up for any exercise is to do that exercise at a lower resistance. For running, I warm up by walking fast and swinging my arms. After walking fast for 5 minutes, I stop and stretch my hamstrings by sticking my butt out, locking my knees, and bending forward with a straight back. Also, I stretch my quads with lunges. After running, I stretch again so my muscles don't tighten and shorten.
2) Head Up
Keep your posture aligned so that you aren't wasting energy holding yourself up. The pain in your shoulder could be from running with a forward lean, which puts tension in your shoulders. Also, as Lady C recommended, keep your shoulders down and relaxed. You may want to ask someone to watch you run and give you feedback on your form.
3) Land Soft
Your shoulder pain could also be from jogging (hitting the pavement as opposed to gliding over it). If you can hear your feet flopping on the pavement when you run, then you are landing too hard. When you run, pretend you are sneaking up on someone and need to run quietly by landing mid-foot as opposed to heel. I run using shoes without cushioning (Nike Free), which forces me to land softly.
4) Stomach Breathe
I get a tight chest when I run sprints due to breathing into my chest (because my stomach is clenched). When you run for distance, you want to pull your breath all the way into your stomach. To do that, exhale forcefully, which creates a vacuum and makes inhaling easier. Most runners breathe with a cadence of 2-2 (two breaths in and two breaths out), 3-3, 2-1, or some similar combination depending on their speed and exhaustion. As far as the previous advice you received to inhale through your nose and out your mouth, I would say that technique is for very conditioned runners (I can't even do it). For now, inhale through both your mouth and nose to reduce inhalation effort and keep your wind.
5) Stride Quick
To move fast, you can either have a long stride or a quick stride. A quick stride is a shorter stride which takes less energy and leaves less room for bad form. Aim for 180 steps a minute.
6) Run Intervals
To help with both form and endurance, try running intervals
(short-distances at faster speeds). I do intervals with a stopwatch, running intervals of 4, 2, 1, and half minute. After running an interval, walk for a minute or two to catch your breath, then run the next interval.
7) Consecutive Days
Rather than running every other day, try running three days on followed by one or two days off. To make progress, you need to overload your body's running systems (both muscular and cardio-vascular). Running every other day may not be enough to overload your systems, especially since you are losing your wind. After warming up, you should be putting in at least 20 minutes of running: either consecutively or broken up through intervals.
Hope this advice helps. You may also try contacting your recruiter for advice since I'm sure he or she has had to prepare others for boot camp. Finally, let me say I am grateful to you for committing your life to protect ours by enlisting in the Navy.
God Speed and God Bless.