In the early Christian Church, followers of Christ suffered great persecution and even death. Many were killed for their faith. That is what is meant by saying someone is a Christian martyr. The way Amanda is using this sentence is to indicate great suffering. Amanda is talking to Ida who has been sick. Amanda is exaggerating in a sense. Of course, Ida has not suffered as greatly as the Christian martyrs did. However, it is in Amanda's nature to exaggerate. She is the exaggerating type. She is full of drama and to use such as sentence fits her overly dramatic personality.
Scene 3 of the play The Glass Menagerie, by Tennessee Williams, is titled After the Fiasco. In this scene Tom explains that his mother, Amanda, is "a woman of word as well as action" in terms of her determination to make ends meet by selling magazine subscriptions over the telephone.
In this particular scene, Tom illustrates how his mother:
...conducted a vigorous campaign on the telephone, roping in subscribers to one of those magazines for matrons called The Home-maker's Companion...
Tom also recalls a conversation between his mother and one of such subscribers who is identified as a member of the Daughters of the American Revolution (D. A. R), to which Amanda belongs.
Presumably, the woman is trying to avoid Amanda's subscription renewal call by replying that she is still sick with bad sinus infection.
Being a typical Southern "belle," Amanda's reaction is to exaggerate her commiseration and use embellished language to express how sorry she feels for her client (although she really does not). This is why she says:
You're a Christian martyr, yes, that's what you are, a Christian martyr!
Basically, Amanda is comparing this woman with a sinus problem with a religious martyr that has been skinned, boiled, quartered, and burned alive in the name of the cause of Christianity: An immense exaggeration, but one that is typical of a woman with the eccentric nature of Amanda Wingfield.