Lots and lots of liner-washing the liner may indeed be what you need. It's not an unusual situation to have some degree of irritation when breaking in a new liner...I routinely have a few days of itchiness when I get a new one. And Neal's right...it can happen even if you've been wearing a specific type of liner for some time. Heck, I once developed a major sensitivity to a liner--an OLD liner--that I'd been wearing for several months!
Now, I never did manage to get back into that old liner (or even a new liner made of a similar material) once I'd broken out in that rash. So if a little time and a lot of cleaning doesn't clear up the problem, you may need to look into getting a liner with a different formulation. While you're seeing if you can adjust to this liner, I'd suggest trying hydrocortisone cream (NOT ointment) on the irritated skin, especially after taking the liner off at night.