This is probably your first baby - because you let her do something in the beginning that was kind of cute, without realizing what this might look like a year down the line! For your next child, think ahead - if the baby engages in a certain behavior now, will it be O.K. in six months or a year if the behavior continues?
Meanwhile, back to your current dilemma. It is not reasonable for you to suffer while your baby nurses. Now that she is a bit older, she is also more secure in the world and certainly in your arms. Unlike a newborn who is a real new comer to the planet -disoriented, overwhelmed and frightened - your baby knows that she is literally in good hands. Now, when you begin to bring in tiny steps of discipline - the occasional "no" - the child won't like it but she will not be harmed by it. She knows you love her. So if you tell her that she can't hold on to your hair anymore, she will be very unhappy about it but not psychologically harmed by it. Because she has paired nursing with hair play, she will be very resistant to changing her pattern. Adults also go into withdrawal when they lose comfort foods (or drugs or cigarettes, etc). We can get really upset. We go into withdrawal. Your baby might also experience withdrawal and so become very fussy and miserable. However, the withdrawal symptoms disappear for babies just as they do for grownups! Once the habit is broken, she will be her relaxed, happy self. To try to help ease the transition, go ahead and offer her other things o hold onto. Can you find her a doll with very long hair? Call it a "nursing doll" and show your daughter ow to use. Exp;ain your reaosn o her.

Interestingly enough, my girlfriend used to let her baby wrap his fist on her long hair when she nursed.  As he got older the only thing that would get him to sleep was to have her hair hang in his face and where he could stroke it.  Problems started when she cut her hair.  Oh well!