All hope is not lost. You can still refinance out, just not as a HELOC. You can get a heloc on your home you live in and then whenever the mood strikes, you can advance on the line. You could buy a car, buy another house, do whatever you want. And you pay it back per the terms of the line of credit. It's like a giant credit card kinda.
But when you get done with this house and you want your capital back, you can still get a refinance to get your money out. It will just be in whatever type mortgage you want like a 15 yr or 30 yr fixed or whatever you choose. There are %LTV requirements, but you will get most if not all of your money back depending on what it appraises for. There are usually seasoning requirements where they make you hold it for a fixed time before you do it, but I just had a bank waive that for one of mine because I paid cash for the house when I purchased it.
Take a deep breath! You're going to be fine!