I think I need a 15 in. (38 cm). I am 5' 2" (157 cm) and 120 lbs. (54 kg) currently due to the quarantine. I am usually 110 lbs (50 kg).
I live in Virginia, sort of near D.C.
I don't really know what kind of saddle. I don't really know anything about endurance.
So, you are a adult and do not need to ride in a 15" child's saddle if English because the measurements will be off in many areas.
A 16.5 is the smallest of adult saddle sizing made in English, otherwise you sit in a child or youth size.
The differences is width of seat, width of flap, placement of stirrup bar and sitting in the saddle not perching on top of it.
If western then a 15" is one of the smaller sized adult saddles.
With your comment part about not knowing what kind of saddle... What is it you are riding in now?
A endurance saddle would probably most resemble a A/P to you, but it is specialized for long rides to give the horse and rider more comfort and support over rugged terrains often times.
So I just peaked at Craigslist for Virginia, picking northern Virginia since you mentioned being nearer DC...
Use the Farm & Garden section, then type in saddles in the search bar and a list of selections appear.
That list can and does change daily...sometimes good finds, sometimes great finds and sometimes absolute junk is for sale. Scroll down the page though because there was a lot in surrounding areas to view, some of which were really nice saddles.
I saw several Collegiate saddles, one of which is Pessoa crafted from when Pessoa was at that company before starting his own...you can see quality.
New saddles that cost $200 are junk, are risky to purchase and the couple I looked at advertised as new are crap and just sitting pictured on the floor you can visually see they are not even and balanced made in panels and leather is cardboard junk...don't do this to you or your horse, please.
I saw some really nice used western saddles too, good brands and used but taken care of appearance too.
Best is if these are local to you, within a short drive you can meet and have the seller bring it to try and return if it isn't a good fit. Do not go by yourself nor have anyone come to your home when alone...always a adult besides you around for safety reasons.
You aren't far out of horse-country where many tack shops are around, knowledgeable people able to help you find and a supply of used should be.
A short distance away are many shops with inventory of hundreds of saddles used, all price ranges, manufacturers and tree widths in every discipline that has been mentioned here.
With the exception of the highest priced saddles, none were out of your price range... best is there will be people at those locations that can help to fit the horse correctly.
I don't know if those saddle shops come to the person but a phone call would give you that information.
Call, be honest with what you can spend and see what they have...my suggestion though is go to the store, sit in several saddles so you know better what size you should be riding in cause 15" English unless you are very petite is just to small. My sister is your size and weight...she rides in a 16.5 - tight 17" A/P English because of length of her femur...
Go to some tack shops and get sized, see what they have in used inventory then you can concentrate on the horses comfort = easier/correct match made.