If you're miscarrying now, you would most likely still get a positive HPT if you took one. So you could check it out by peeing on a stick if you wanted.
When an early miscarriage progresses without complications, there is really not a heck of a lot that anyone can do. If you went to urgent care, or your doctor's office, they would mostly be able to say how sorry they are. They might offer you painkillers (no guarantees). In your plan (wait and see, go to urgent care if you feel worse), you don't pay for the sympathy of trained medical professionals - not a meaningful difference. It's a fine plan.
If you start to run a fever, or if you're getting through more than a pad every hour or two, go in. Otherwise, stay comfy.
I'm sorry you're going through this.
ETA: Most OBs will get a suspected miscarriage in for an urgent appointment the same day. So if you do want to call yours on Monday, you may not have to wait that long to see someone. However, my experience was that seeing my doctor took the thing from "I may be having a miscarriage" to "I have had a ton of ultrasounds, and I may be having a miscarriage." They can do a lot to identify what's going on, but if you are having a miscarriage, it's not like they can do something to stop it. They'll do what they can... but it may be that all they can do is tell you for sure what's going on.