Myra was introduced during the show's fourth season as a potential love interest for Steve Urkel. At the time, the object of Steve's affections, Laura Winslow, was dating Ted Curran (Patrick J. Dancy). Much to Ted's dismay, Urkel was constantly putting himself between them, going as far as donning disguises, so that he could "chaperone" their dates. Laura thought that they needed to find another girl to occupy Urkel's time, but admittedly couldn't think of one who would "give him the time of day". Ted realized that his cousin, Myra, liked brainy guys, and suggested that they set her up with Steve in an attempt to get him out of the way. Steve reluctantly accepted what he assumed would be a dull blind date, but was pleasantly surprised to find that Myra was as beautiful as she was intelligent.
Like Steve, Carl also occasionally lost his patience with her and frequently yelled at her as well.
As their relationship progresses, Myra becomes obsessed with Urkel (so obsessed that she has pictures of him all over her bedroom, similar to Urkel in the earlier seasons), and develops a rivalry with Laura. Often, Myra would be very jealous of Laura, and accuse her (inaccurately) of scheming to take her "Stevie-kins" away from her. Laura, however, thought of the accusations as annoying, and tried—not always successfully—to ignore them. As for Steve, he became very repulsed by Myra's jealous and possessive nature, which were both explored in seasons 5 and 9. He has tried not always successfully to get her to leave him alone, implying that Steve has finally realised what life is like in Laura's shoes.
During their relationship, Myra often demanded full loyalty from Urkel; in turn, he tried to stay true to Myra, despite his still often overwhelming feelings for Laura. She also became upset when Urkel turned himself into Stefan Urquelle via a "transformation chamber" (in his bid to win Laura's heart). She felt he was a joke, and liked Steve just the way he was. At one point, she tampers with the transformation chamber, thinking Stefan will use it to return to Steve and realises her mistake when she learns Carl Winslow was in there to fix his dwindling eyesight, turning him into an "Urkel-clone" known as Carl Urkel. Despite her faults, Myra tried very hard to please Urkel and others, including the Winslows.
By the last season, with Laura finally realizing that she has feelings for Urkel, and it caused both him and Myra to grow apart. In Seaon 9's Breaking Up Is Hard To Do, he learned that she hated his makeover and demanded that he return to the "sexy" nerd she loved so much, suspenders and all. When Steve refused, Myra broke up with him first and it later turned out to be a ploy to get him to renounce his love for Laura. When that failed, she resorts to not only suing Steve, but also stalking and spying on him with illegal surveillance gear and going so far as to install a special device in Urkel's eyeglasses that allows her to track his every move. She recruited Stefan to help her stop Steve and Laura's first date as a couple. Though initally successful, Myra realises that she still wanted to date him and vowed never to rest until he dumps Laura and takes her back. Urkel eventually finds out and is outraged with her for violating his privacy. He demands that she relinquish her love him and leave him alone because he will never take her back. Myra refuses to relinquish her love and dressed up as Laura and went as far as getting her arrested for stealing her watch. However, Urkel was able to drop the charges against his girlfriend when he exposed Myra for stalking him with illegal surveillence gear. The police confiscated everything and pursued criminal charges against her. When Myra learned about Urkel and Laura's engagement, she makes one last bid for the object of her affection when (after learning Urkel's life is endangered during a space-walk) by posing as his fiancée during a news broadcast, which failed to win him back. It's assumed Myra went to jail for her crimes in stalking Steve with illegal surveillance gear.
If the show had continued in its final season, it would have been revealed that Myra has continued to pine away for Steve and attempts to stop his and Laura's wedding even with Stefan trying to stop her. While hanging out with Myrtle, she eventually found love with the Urkels' cousin from Detroit, Cornelius Eugene Urkel (OGD), who accepted her the way she is and helps her move on with her life. Myra would also accompany him during a tour across America to teens in similar positions and his reforming could show them that they could make it in this world. She and Cornelius would, before leaving, witness the birth of Stephanie Laurine Urkel, Steven and Laura's daughter. However, the storyline may need to have been rewritten or a new actress would have had to portray Myra as Michelle Thomas was diagnosed with stomach cancer in August 1997 and died in December 1998, five months after the end of Season Nine.