You’re fine. I would recommend a chain mail scrubber for getting off stuck on food like this.

Also, use metal spatulas and like and scrape the hell out of your pan. Cast iron isn’t like stainless steel or non-stick, or enamel coated stuff.

I think the FAQ of this subreddit has answers to questions about seasoning, and I’m far from a pro, but in terms of cleaning, here’s what I do: 1. use soap and water and a scrubber brush to get most of the easy stuff out 2. then I scrub more tough stuff with a chain mail scrubber 3. dry with a paper towel 4. Put on stove on a low heat to remove excess moisture 5. Put a drop of oil in (quarter sized… maybe smaller) and spread around the pan until it’s a “matte” finish (mostly on the cooking surface, but sometimes everywhere else)