The longer answer is, unlike residency where the are often a ton of applications and PDs likely don't have time to review LORs/PS in depth prior to offering interview, fellowship applications involve a much smaller pool. Yes, I know pain is pretty competitive but it is still a much, much smaller subset of people than a huge specialty like Psych.
Because of this, your application is much more likely to be considered as whole including LORs (which have a greater impact since it's a smaller field, increasing the chances of docs actually knowing each other) and personal statements. It's an foregone assumption that you have done several electives in the field - how else would you develop (and confirm) interest in the field? But including this as work experience is absolutely wrong - if I am applying to critical care, should I include my 2 months in the ICU as an intern, or my extra month in the cardiac ICU this year? No way, it's part of my residency and I will have gained a letter from these rotations.
I know it's awkward not having much to put in "work experience" but know that you are hardly alone - most people haven't had side jobs in medical school or residency. Some have taken time off between residency and fellowship, and that is predominantly what this field is for.
