There is alot of info already posted concerning breathing, that should help you there. The words you use for breathing, push, suck, push, push,,,,sound a bit forced. Perhaps it's just your description, but soften up a bit, if not. Relax more, and try to make it more natural. "Pushing" the chest in sounds forced. It should be natural and more relaxed breathing. As both Margaret and myself have said in a recent post, relaxation is key. Especially for you. In the beginning, or anytime, relaxation , and a feeling of opening up, aids all aspects of practice. If you really relaxed, your neck pain would "change" immediately. It might not disappear, immediately, but you can produce a change, or shift, with relaxation, that would lead to clearing that blockage. As you are studying so much and creating tension there, you might have to take frequent breaks to relax for a few minutes. With intense work that effects your neck, sometimes, you have to hold your own, do the best you can to maintain, until you get a chance to recover completely. How much time you are doing "good" for the neck , versus neck abuse. If you incorporate the active exercise in a daily routine, you can get to a point where you can manage neck pain , and keep that area completely open , on a daily basis. I will list a few neck things to try, for short breaks from reading/studying.
1) Sitting, relaxed. Let your eyes gaze downwards (@45 degrees). Focus on relaxing your eyes. Any eye tension/strain can tighten the neck and add to closing that area. Drop and open up the tops of the shoulders, relax the top of the spine. Move energy down to your palms as you relax your shoulder area. If you have the extra minutes, after you relax the neck shoulder area/ out to the hands, focus on the lower dan tien in that relaxed state and move the energy/relaxation process down to the bottoms of the feet. In general, these things move energy, relax you, open you up, move tension/blockage out of that area. Use your mind to envision stress, tightness, etc., leaving. You can envision a sun or bright light in the top of your spine, shoulders, burning off blockages and energizing the areas.
2) Don't rub your neck. It can be the opposite of moving energy through or away from that area by relaxing and focusing on palms/feet from the above sequences. It like putting more energy into a blockage, that you don't need. "Only" , if you are aware of what you are doing energetically, could you self massage that area and open it up. Notice I say massage, as opposed to rub. Deep pressure with knuckles or fingers, in combo with relaxing , can, open up the area too, but not rubbing.
3) Again, in a sitting position: Roll the neck down. Think of the image of a fan, spreading, or fanning open as you "roll" down. Basically, I am saying bend your head down, but not in the sense of crimping or cutting of energy flow. Pull through the crown point as you roll down the neck, spreading that fan, opening all those vertebrae, releasing energy trapped in the vertebrae. Again , you can visualize energy being released as you do this. After this relaxed stretch and opening, try coming back up, center your head/neck, and very relaxed/softly do the neck circles Master Lin does after meditation, or in harvesting qi. Horizontal circles left and right, and dolphining the neck. Consciously releasing the blockage tension is better first, so you are more open when you circle the neck.
3) frequently twist the spine, with your head looking forward, again , from harvesting qi exercise..
4) Using sword fingers through the throat area to break up blockage in the C7 / top of the spine area in back. Visualize it leaving/releasing, or literally grab it out with your hand, again from the front side, and throw the energy you grab out into the ground, knowing it is leaving your hand, and going into the ground. Grab softly, slowly with feeling, visualing yourself grabbing out the blockage. Lastly, hold your Palm by the base of your throat, and send healing energy(visualize) to the area in back you cleared. Warmth, relaxation, sending qi through the palm. I am assuming you are doing level I. This gets into level II, with a few parts missing, but it will still help.
4) You can get up and do a movement like touching your toes. Keep your back straight as you go down to waist level, lead the movement with your heart area(aligned to the earth), then relax and hang down as you reach the bottom part of the movement. Again, like the neck roll, this time think of the whole spine, pulling through the crownpoint, with gravity assisting. Also the earth. Let it all release into the earth. Just hang there a bit a let your vertebrae spread and open. When you come up, roll up one vertebrae at a time all the way up to the crown point. Exhale as you roll down. This is hard to write a description of , but hopefully it will give you the idea of what you are doing. All I have mentioned as to do with opening up, relaxing , and moving energy.
5) Being aware of your alignment as you study. If possible keep you spine straight, crown suspended as you study. Breath correctly as you study. You can be exercising , in a way as you study. It's like the idea of gung fu, or kung fu. Work/skill. You can do kung fu doing anything. Cooking, mowing, studying, etc. It is a matter of alignment, awareness, breathing...Same for qigong. You can be doing it as you preform a task, or, all the time.
Even if you do the whole level I exercise, neck pain may not leave immediately. Usually, it should be completely gone by the end of the exercise, once you have a daily practice established. You can clear this completely on a daily basis. Maybe focus more on your neck, after you finish studying, so your healing/recovery extends into down time. As you go to bed, call on the master's energy , to help you rejuvenate as you rest, and to help you get through your work and care for yourself. Be open to insights and ideas of what is best, to do when, as you study. Qigong can help you maintain through difficult work periods.