让我来介绍一下自己。 让我做个自我介绍。/让我自我介绍一下。 请允许我做个自我介绍。/请允许我自我介绍一下。（formal）

It's better to say"让我做个自我介绍。"or，alternatively，on a less formal occasion，“让我自我介绍一下。”I wouldn't say what you wrote is utterly wrong，but it sounds a bit awkward to my ears.And normally Chinese speakers wouldn't say it.

The only way I can think up when your saying might be proper is when you stress "Let meeeeeee introduce myyyyyyyself",meaning you don't have to do that on my behalf,"让（！我！）自我介绍。"，in normal,you should use what I just told you to "relax "your sentence a bit.

yes, it's correct

Hello, you can say “我来做个自我介绍吧！”.This is very common and relaxing~