Don't panic... cholesterol of 237 is not that bad... it's not good... but not that bad. You will not kiel over and die...
To contrast... 20 months ago, my cholesterol was 328, Triglicerides 304, LDL 222, and HDL 46. I have since reduced these numbers 50% and I'm now in the normal range.
Keep losing the weight until you are in your BMI normal range. Sounds like you are doing a great job! Keep it up! This will help your health in more ways than you know.
Now for the not so good news... weight and diet is extremely hit and miss with regard to cholesterol levels. This is because your liver produces nearly all... if not all... of your body's cholesterol.
Weight and diet has never helped my cholesterol numbers in my 16 years of dealing with high cholesterol numbers. In fact... when I did a vegan diet for 9 months... my cholesterol went through the roof. To contrast... when I did Atkins for a year... my cholesterol numbers improved ever so slightly, but nothing to speak of.
You will find plenty of skinny people with very high cholesterol.
Ask your Doctor about Niaspan. It's prescription Extended Release Niacin (Vitamin B-3). This is what I take and is what reduced my cholesterol number 50%.
Best of luck.