I had a diagnostic lumbar puncture several years prior to my t onset as part of a chronic headache workup (? Benign intracranial hypertension). I cant comment as to whether the LP will worsen your symptoms. You need to weigh up the pros and cons of your situation.
Results were borderline.
I ended up with a post dural puncture headache that landed me back in hospital 3 days later, but spontaneously resolved (didnt need a blood patch).
I opted out of any further investigations at that time.
My headaches have completely disappeared in my 40s with copper chelation and work on my liver, gut, and hormones.