Do I need to lose weight?Short Answer:
Barring an unusual condition..... you're not fat, not even close.
I'm not a fan of BMI. Why?
Because it makes no attempt to measure, model or estimate body shape (ie body fat)
So with an 'in range' BMI, a person could be fit or fat.
At 6' / 205 I have a rather high BMI, with a 40" waist I'm kinda fat. At the same weight (same BMI) but a 35" waist I'm much fitter (lower body fat)
So any metric that neglects body shape lacking, it's easy to use but of less value.
A better metric is waist to height ratio. Suggested max for men is 50% (college swimmers are 42%)
For women suggested max is 45%
Your number is ~43% which is quite good.
Of course, this is just a simple estimate, but imo it is much better than BMI.
OTOH, waist to height ratio w/o a weight number can be misleading as well. But you have a decent weight, not overly light for your height, as indicated by a mid range BMI and coupled with your waist to height ratio ... you're not fat.
Here's a link for an online calculator that does BMI, Waist to Height ratio and other things. Play around with your numbers.
Body-Mass Index, Waist-to-Height Ratio and More...