I had jaw and tooth pain from the styloid irritating my trigeminal nerve, I had a tooth re-filled where I was getting the pain, but it wasn’t that! There are some medications which can help with nerve pain- I take Amitriptyline which helps, otherwise there are medications like Gabapentin, or Carbamazepine. They can take a few weeks to build up in your system, so don’t always work straight away, and sometimes you need to try different ones to find the right one. Heat or ice can help too, & some members have found lidocaine patches or gel on your neck help- I’m not sure what’s available in Germany though.
As @Isaiah_40_31 says, your doctor is wrong- average length for styloids is 1.5 - 2.5 cms, an average length styloid wouldn’t reach to the C1/ C2 level which yours do, and we know that the angle can be just as important as the length, so your styloids could certainly be the cause of your pain, don’t be fobbed off, you are on the right track!
There’s more info here about medications etc:
ES Information- Treatment: Pain Relief, Medications and Alternative Therapies - Welcome / Newbies Guide to Eagle Syndrome - Living with Eagle
And thank you for translating your posts, as the majority of members speak English on here that’s what we go with, & you’ve certainly made it easier for us! 
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