Can I get an epidural steroid injection if I am allergic to ivp dye?

Yes. Some radiologists use a dye to confirm placement of the steroid injection but this is not mandatory. Just tell them about your allergy and they can perform the injection without any contrast.
Yes. There is another dye the doctor can use called gadolinium dye for the injection. Alternatively you can be pre-medicated with Benadryl (diphenhydramine) the day before and the day of if that dye you are allergic to must be used. Usually the doctor should have the gadolinium dye on hand.
ESI. Iodine dye is used to verify needle placement in the epidural steroid injection. If you have allergy to ivp dye, your doctor can use different kind of dye. You can get epidural steroid injection with allergy to ivp dye.
You don't dye. If epidural is not transforaminal by an experienced doctor.
Yes. Esi involve the insertion of steroid into the space outside of the dural covering through either the translaminar or transforaminal approach. Although "dye" is use for location, it is not essential to safely perform an esi.