Make sure you have more than enough time to give the medication, i.e. Not just before you're rushing out to work and are therefore a little stressed yourself.
Carefully have everything prepared and to hand before you start.
Dim the lights or close (or partly close) the curtains if in the daylight. Have some soft noise in the background.
If possible try to have one person holding her and another administering the medication.
You can try to see if gently covering her eyes with the towel will help calm her down a little.
When holding, there are different methods. Whichever you choose, just be sure that the bird's chest isn't being squeezed.
One suggestion is to place the index finger on one side of the neck, middle finger on the other side to minimize movement, thumb bracing his side,and other two fingers lightly laying across the abdomen of the bird. Take care not to squeeze her chest.
If you're right handed, hold with your left hand and give medicine with your right. Try to keep her more upright than flat on her back. With the bird facing you, take the syringe and angle it at the side of the beak on your right, pointing to the bottom left corner of her mouth. If she's screaming, that's perhaps easier, as you can get the syringe in. Depress the syringe slowly, don't rush as it will likely mean the full dosage doesn't go down.
It isn't a pleasant thing to do but you will get better and quicker over time.
It sounds as though, as soon as she sees the towel, she knows what is coming! You said "no matter how long I wait for her to calm down she will just scream and scream. ", therefore, I'd advise you to 'just get on with it' as currently you're actually just prolonging the stress by waiting for her to calm down, when she won't - makes sense?
Prepare the medication outside of her room, then come in and as calmly as you can, catch her. Talk gently as you hold her and administer the meds. Try to act calm and confident, and get it over with quickly (just don't rush plunging the syringe).
Tell her 'good girl' as you return her to her cage and give her a little reward (ball of millet?) afterwards. It'll help you feel better too
Other members may have other tips to pass along.
Hope it becomes easier soon.