Hello-I just signed up for this forum to answer this question. You most likely do not have Sjogren's Syndrome. It is more likely that you have rhinitis. This is usually caused when weather conditions become dry, or by indoor allergies (there are two types of rhinitis). It sounds like yours is caused by the dryness in your home? If you have the allergic type, wash you bedding lots (dust mites cause big issues, especially in your duvet and its cover).
I get symptoms of this in the winter because the heat dries out the house. I purchased a diffuser. A diffuser blows cold moist air, versus a vaporizer which blows warm moist air. Cold air vapor is better for you, and most diffusers make negative ions which help clean the air in your home. Buy one which holds 500 ml, or you will be filling it constantly. I bought two diffusers. One for my bedroom, and one in the Living room. Amazon had them cheap.
Secondly, I tried all of those nasal sprays, they dry you out more. What you need to purchase is a nasal spray which has 100% natural sesame seed oil. Use this spray three times a day, and it will help with your dry nose. Also, drink lots of water, avoid alcohol, caffeine, spicy foods, and things like ibuprofen, as they all act to dry you out more.
I suffer from this as well. It sucks. If you can't afford diffusers, in the very least try the sesame seed nasal spray. I think that will help you significantly. Take care.