I also have had a negative NHS test. I've been wondering the same thing.
My guess is that I could find a positive blood test if I had enough money to keep getting different tests. There seem to be false positives and false negatives. I don't want to cause offence by saying this as I realise this is a rather hot topic. I think everybody needs to find there own place with this.
Then, if I did find a doctor to treat me, I'm not sure it's worth the stress of treatment. We all have our own individual ways of dealing with this and all our own lives to factor in.
I may have chronic Lyme. I may not have chronic Lyme. I might get better with treatment. I might not have it and push myself through something I don't have the energy for.
I don't have an answer right now, so I'm doing nothing. Maybe if I had the funds I'd feel differently! In some ways it feels easier that I don't as I would be scared of opening up doors I don't have the wherewithal to get through.
I'll be interested to follow your decision and best of luck