Thanks for the well wishes, everyone!
The last few days were rough, healthwise, but today is looking better.
I have already received a new interview date—April 11th. So, I was right with my time frame estimate of 4-6 weeks, and I'm okay with it. It's nothing in the grand scheme of things.
I was a little nervous about the rescheduling process, but in the end, it was super easy. I called the USCIS Contact Center number listed on my Interview letter less than 24 hours before my interview. I told them I was sick and needed to reschedule. They asked if this was my first time rescheduling, and once I confirmed, they said it shouldn't be a problem. They take note of your request to reschedule and forward it to the field office. I was told that if I didn't hear from them (the FO) within 72 hours, I should call the Contact Center and ask for an update. The following day, even before my original interview time, I already had a new interview date.
I asked my doctor for a note and confirmation of my COVID diagnosis, just in case, but I wasn't asked to provide anything. I'll keep it on hand, just in case.
So, just a small bump in the road, and as @BeautifulAmerica said, at least the weather should be warmer for the oath ceremony! 😃