Here are my two cents as well.
You will need to wait at least 6 months before a refinance or equity draw. Many lenders require a 12 month "seasoning."
You really need to talk to a qualified real estate agent to get an accurate idea of the market value of the property. If you personally pay for the appraiser, you cannot use that for financing. The lender will have to order their own (meaning that you will pay for it twice). They do that to prevent having your "appraiser friend" do you a high value favor.
A HELOC or any other equity drain is going to only allow you to withdraw up to 80% of the equity. If you did not put any money down, you are going to need at least a 25% increase in value just to draw off a few thousands (not factoring the loan fees).
That being said, why not take what you would be paying on your HELOC and put it in a savings account each month. You will be surprised how quickly you will have a down payment and without debt to boot.