No, birthing centers do not offer epidurals. They can sometimes offer pain relievers if they have a doctor present and on staff but an epidural involves needing an anesthesiologist. Go tour some birthing centers and ask questions about what they do offer. Then ask if you can have a private tour of your local hospital. Explain that you have social anxiety. They can make special accommodations for you and your situation if an epidural is important. Congratulations on your little one! Good luck and best wishes.

There are lots of different levels of care in "birthing" centers.
Most offer some sort of pain management techniques, and have the ability to quickly and efficiently deal with any problems that might occur.
I'd encourage you to visit and check out your local options. You might find that a local hospital has a maternity wing with private rooms for labor and delivery. Or that the birthing center is all inclusive and has an anesthesiologist and ob on staff. You should also discuss your options, and your ideal birth vision, with your obstetrician and/or midwife. They, of course, are the best resource to find out what is available in your area.

I definitely agree with touring a few different centers before making your choice. Birthing centers are usually more geared to natural birth, but some may offer some type of pain management. An epidural requires an anesthesiologist administer the medication, so I doubt you will find a center that can accommodate that type of procedure. There are other pain control options, so make sure you ask each center about what types of options they provide. You may also want to ask them what their transfer rate is and what they do in emergency situations. You may find you like the more laid back approach with a birthing center, some let you labor in birthing tubs and some will really help you feel relaxed and encourage natural ways to deal with the pain. But, you may find you want to be close to a hospital for emergencies. It doesn't hurt to tour the hospital as well, some hospital rooms are very nice today and some of the staff are very helpful with natural births or offering a more laid back experience and you would have an epidural option in most hospitals. Just tour all of the places near you, ask questions, and choose the place that you are most comfortable with. Best of luck!

Thanks :)