Yeah!
And don't ask questions about anything! Never ask a forum for advice!
Deal with your social anxiety, and all of the problems that go with it, on your own! This forum is for posting cute pics, not for helping each other!
Yes, because the advice OP has received so far is helpful, realistic, and approved by evolutionary psychologists around the world.
Lying to get into a relationship is stupid, especially if you're looking for a real relationship. For one thing, if you've never have a girlfriend due to SA-related issues you can't possibly act like you have. For another, if the woman you approach is somehow gullible enough she will find out about the truth sooner or later. In a best-case scenario she might shrug it off, but most likely she'll lose her respect for you. I don't know how how attractive or unattractive male virgins are to women, but when it comes to dishonesty I think we pretty much have a consensus.
Of course, if your goal is merely to have an experience and you don't care about your woman as a person, feel free to make up everything from having an ex-girlfriend and having an investment. Chances are the women who are attracted to you are attracted to you for the wrong reasons and it might as well - you two probably deserve each other.