Any advice for when an insurance adjuster goes completely silent?

I got rear ended about a month ago. It wasn’t a massive crash but enough to mess up my bumper and neck. At first the other driver’s insurance acted like it was going to be simple. They sent an adjuster out, looked at the car, and said everything would move fast. Then suddenly my adjuster went quiet. No callbacks, no updates, and now every time I call I get bounced to some random rep who says “someone will reach out soon.” Spoiler: no one ever does.

The body shop did what they could, but the car still doesn’t drive right. Plus, my shoulder’s been bugging me since the accident, and I’ve started thinking I probably rushed into assuming it was minor. I haven’t signe͏d anything yet because the whole thing feels sketchy. I just don’t want to get stuck paying for stuff down the line because they dragged their feet.

From what I can tell, my next move might be asking for a supervisor or possibly sending a written request to confirm the claim’s status. I read that sometimes a formal compl͏aint to the state’s department of insurance can get them to respond. Has anyone actually done that and seen results?

Someone I know mentioned Slaughter͏ & Lupton helped them figure out what to say without hiring them outright, which made me wonder if that’s a smart step before escalating. I’m honestly not looking to sue or anything, I just want them to do what they said they’d do.

For those of you who’ve dealt with this before, what actually gets things moving again? Is there a magic phrase or department I should ask for when the regular adjuster stops replying?