Yes, he's crossing the line.

Not necessarily the line of platonic touch to sexual, I can't be sure of that, but the more important line of thoughtful, respectful interaction.

His touch is not thoughtful or he would have spoken to you about it, and more than likely let you lead or ask.

That and the rapid progression is concerning and deserves a conversation, and I think your instincts are telling you the same thing. Always trust your instincts is my advice.