I actually had a stuffy nose and mild cold right around my missed period date. Gynac told me pregnancy hormones can cause nasal congestion, which is quite common.
Yes, our immunity drops slightly after conceiving, which makes us catch a cold easily. Just take plenty of rest and drink warm water, you will be fine.
I totally understand how eagerly you are watching out for every single sign. A cold can sometimes happen due to hormonal shifts, I really hope this month brings you good news.
It can sometimes happen due to low immunity, but please don't take any OTC cold medicines. Better to wait for your missed period, do a test, and check with your gynac first.