Hotels do get greedy. Do you have Hilton status? That helps. The largest factor will be the hotel's reputation. Do you happen to know who owns it? Is it a Hilton-owned hotel or is owned by a unethical place like Aimbridge? That is not to say even all Aimbridges are terrible, but more likely to be greedy.

My Hilton app shows my upcoming stays; yours should too.
You should have received an email confirmation with a number.
Endure chatting with Hilton via the app. Tell them your email confirmation got cut off in your email app and you can't read part of it, and can they please resend it? Do it in the app because writing. Save it.
And yes, show up even before check in time, even though your room won't be ready.

Where is this hotel, if you don't mind saying? Big city like Dallas or tinier area?

I would not worry, but I would also be proactive. I am amazed by what even Motel 6s charge for 4 minutes.