Hello @learningstudent. Welcome to Mayo Clinic Connect!
I have had similar experiences in the past that matches your description. Most of these instances happen during winter, and early spring for me. When breathing, I'd feel cold air entering my left nostril that will cause a sharp headache, numbing on the left-side of my face.
Here's a bit of my background so you can understand my situation/solution to these symptoms better. I was diagnosed with mild asthma, sinusitis, and I also have a deviated septum that cause some difficulties in my breathing. When the symptoms above first started, I went to the doctors and was told that any of my preexisting conditions could have caused them, essentially saying that the cause of my symptoms was unidentifiable.
However, he did recommend some solutions that I found helpful to alleviate the pain, and reduce the frequency of these symptoms. Firstly, having a humidifier placed next to my nightstand while I'm sleeping had stopped the cold-air-breaths at night, and lessen the symptoms during daytime somewhat. Secondly, I've been steaming my face with hot water + a few drops of lemongrass oil for 5-10 minutes almost every night, and I found that this works the best to lessen the symptoms.
Please keep in mind that while these solutions work for me, they might not deliver the same result to you. It's best to consult with your physician before trying new solutions. @learningstudent, how long does each experience last? Do you also experience headaches during those times? Have you mentioned these symptoms to your doctor?