Another anxious patient here - I recently had a back tooth out after a failed root canal. No expert, but my tips are:
Tell the dentist you're scared/anxious/nervous. I felt embarrassed admitting this when I first saw my dentist (I'd seen the same person for years, then she went on maternity leave and I was really afraid of seeing someone different. After my original dentist came back I actually stuck to the new dentist.) but she said she would rather know, and is super-kind and patient. I honestly think they see all sorts.
The dental nurse holds my hand during the injection. Initially she offered and I was mortified but grateful - now she just does it automatically. During my root canal I needed the anaesthetic topped up numerous times and almost broke her fingers, even though I couldn't even feel the needle.
I prefer to have everything explained as it goes along, plus time checks - now I'm going to do X, we're almost there, another ten minutes and we'll be all done. I know others might prefer blissful ignorance though!
It also helps me to know a timeframe if possible. When I had the root canal it was a one hour appointment so as I went in, I to,d myself that at 3.30 I would be walking out and it would all be over.
Don't be afraid to ask for a break. My extraction was "difficult" and midway through I had to stop for a breather. Agree a signal in advance - my dentist gets me to raise my hand.
This is probably really shameful - I am 44, usually a sane person - but I took a stuffed toy to the extraction and held/squeezed it.
I agree re lavender oil - I just rubbed it under and inside my nose. I do this before bed most nights.
If it's an option in terms of money/distance, consider a taxi home - after my tooth was out I felt exhausted and just wanted to get back as soon as I could, not faff around waiting on a bus and having my frozen face in public. The receptionist should have a list of taxi firms and can call one if you ask.
Good luck!