Overstayed and new visa?

Okay, I know I was kind of stupid.
I came on a visitor visa and have overstayed for almost 3 months. Now I found a school that will provide me with an ARC. They are already processing it. I think I have to get out of the country to get a valid visa to get my ARC. Am I right?

Now I am really concerned that I wont be able to come back once I left. Can it happen that I wont be allowed to enter with a new visa? I will go to Thailand this week to get a new visa.

Has anyone experience with overstaying and getting a new visa within a few days? I`m thankful for every answer.

A friend of mine overstayed and got a new visa and has now got an ARC. However he only overstayed by 1 or 2 days so it was a little easier to explain.

Update for everyone who gets in the same situation:
I overstayed 80 days, paid a 5000 NT fine and had to show a letter from a friend where I am staying together with her ID. I also cannot get into Taiwan visa-free for one year.
I went straight to the embassy in Bangkok and applied for a new visitor visa. I again gave them a copy of my friends letter and of my flight ticket. I got a new 60 days visa. No problems.