The mucus in the back of your throat is probably from postnasal drip, due to either inflammation of the nose, called rhinitis, or sinuses, called sinusitis. One of the causes of rhinitis and sinusitis can be allergies. Once identified, avoidance of the substances that cause the allergic reaction, if possible, is the best. But many times, identification of the allergens is not possible. In that case, treatment of those usually involves doing nasal washes. Often this is followed by a prescription nasal steroid spray. A nasal steroid spray does not provide immediate relief of symptoms. It may need to be used every day for several weeks to months for it to help. To get the most out of a nasal steroid spray use it after doing a nasal wash. A nasal wash helps remove mucus from the nose and sinuses. Please read our nasal wash treatment information at http://www.nationaljewish.org/disease-info/treatments/alt-ther/nasal-wash.aspx to learn more about this technique. Share this information with your doctor to see if you would benefit from this daily treatment.
Don't worry about the long pauses between breaths. It could be the result of your taking deep breaths on a regular basis, related to hyperventilation, and there is no danger that your breathing will stop. Persons with a sleep disorder, obstructive sleep apnea, do stop breathing for long periods of time, when asleep, and this is often associated with bad snoring. As for difficulty inhaling, the most common conditions associated with that are chronic nasal obstruction due to mucus or a deviated nasal septum, and a condition called vocal cord dysfunction (VCD). You may want to discuss that with your doctor and your doctor may want to do pulmonary function tests. The test should include what is called a flow-volume loop, both inspiratory and expiratory.
Have you been seen by an "allergist" that also specializes in asthma to rule out allergy? This concern is something that should be discussed with your doctor.