In a radar environment, the problem is very easily and very quickly solved.
You can only get yourself into more trouble by staying quiet. One of the things the inspector who has a chat with you (after you get down) will want see demonstrated is responsibilty. If you made a mistake, quickly fessed up, learned, moved on, you will come out of it much better than trying to 'get away' with something.
I once heard the FAA claimed the average time before a non IR pilot lost control of the aircraft when confronted with IMC was 45 seconds! (I think it is automatically a Distress Phase???)
Just for interest: I have had a pilot in exactly the situation you describe, except it was a non-radar environment. He was trapped in a valley which he thought contained a strip. His options were to land, or climb thru the thin layer until on top of cloud. We recommended he land, but on his inspection realised it was not a strip and was unsuitable to land on. We confirmed he was not where he thought by ringing someone at that strip and asking if there was a cessna circling. So he was lost, in and out of cloud, and beginning to panic. He had a lot of endurance, which gave us some options. We got an experienced pilot who was a controller to talk to him about what he had to do (maintain vis with terrain etc), what instruments he had etc. which helped calm him, while we rang around police stations etc trying to pinpoint his location. Eventually he found a gap in the cloud and climbed on top. Meanwhile, all the RPT traffic in quite a large area were grounded while we sorted him out. Eventually he got high enough to receive a ground aid, and he got talked all the way to a large airport (he was nowhere near where he thought). No-one complained about the delay, he wasn't charged with anything, and I'm sure it saved his plane, and maybe his life. It made our day a bit more interesting, too.
Moral: Speak up.