Are you talking about donating an egg to someone else to use and keep, or about having one of your eggs carried by a surrogate so you may have a baby? Both things are probably possible.
Please only go to the best that you can find with that type of procedure. You hear people all the time deciding not to release the baby to the family after it is born because of becoming attached to the baby. And it becomes a huge mess. Also if you have a female friend that you trust VERY VERY well could also help you with that process.
Best of luck on having a baby!
Yes, you would need to find a surrogate mother to carry the baby after it has been fertilized with DH or donor sperm.