Try a 1 mL blunt needle syringe to bypass hair and apply it directly to the scalp. Once you got it on the scalp where you want it then use your fingertips to massage it into the scalp. Here is a link for the syringe if needed. https://www.amazon.com/Duda-Energy-SyringeBox001-Industrial-Syringes/dp/B01AFVLE76/
https://www.amazon.com/gp/product/B01AFVLE76/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
Those are the ones I bought and I just kinda assumed, like you did, they were all sterile. In the description, it says they aren't.