In floortime play therapy or sensory Ot style therapy, we start with "following the child" and moving the child a bit at a time.
You may have to let her hair be very dirty and pull it in a pony for a week or two :). You may want to start by talking about that you guys are going to bathe and not wash hair for three days (which may end up being many days, but just pick a number and don't go before it), but you guys have to play with your hair dipping it in the water and washing your hair but not hers. Ask her to please not get water in your eyes, because it scares you a bit. After you dip your hair, tell her "wow, that did not get near my eyes". Then let her cover your eyes while you gently dump or spray your hair. Then let her do it to your hair. Then just bathe her body, next time do the same thing, but warn her before you get in that this time after she washes your hair, you guys are going to just dip the ends of her hair in the water. Don't talk her into it, just say it somewhat matter of factly. Make sure you get a feel for where the break point is and don't go all the way there. Approach that point over and over just a bit further until you can gently get her to agree to approach it. You will get to a point that you will know when she will get upset, support her, retreat, and then push in again. Patience is of course a necessity. The best part is that you will become her partner it, not her adversary. It will build trust in many ways other than hairwashing. Oh, one more thing you might do, if, before the period you define, she says she will wash her hair, be very careful to take her up on it. Say, well, maybe we just wait one more day? Be sure you are not going to set the process back. Just something to play with when you are in it.
If you must medically continue the eye drops and cannot use this method, then use techniques like letting her do it to you first. Make sure you explain that you are a bit scared and you need her to count to three and keep counting while she does the drops. Say "wow, the counting really helps me know how long I have to open my eyes". Start slowly by getting her to close her eyes and maybe use visualization to work through like " Close your eyes and imagine we are going to do your drops, are you a little scared - yes, I know, but mommy is here. Lets wait a minute, now imagine we are all done, how do you feel now, yes, better, does it hurt now?". Then move the visualization to "Imagine we are going to do your drops, we are counting now, how much longer - oh, yes, we only have to count to 5 before it is over. Now imagine it is over - is it all better now". Move slowly until you get her to visualize the drop hitting her eye, but she is counting, how much longer? - you will ask. etc...
I know this hard to get accross in the mail, but the main point is to start where she is, help her see the other side of the fear before she experiences it. Support and stay with her, try not to oppose her. Irrational fear cannot be worked through rationally, it must be done with emotion and with love.
I hope some of that works for you. If you cannot make it work, you may seek a great OT who understands sensory support (www.floortime.com) to help you.
J.