Take a deep breath, your doing a great job. Its very hard when our LO's have reflux. I well remember going through the same thing. No don't leave her cry. CIO is not recomended and honestly I think it would only make things worse for you. You have a few issues here, nothing that can't be worked through, but its going to take time and consistency, thins wont be easy, but it'll be well worth the work.
First thing we need to get your DD (love her name btw) onto a good routine. Start with a 4 hour EASY to start. If she feeds at 4 hour intervals she'll get all the water and calories she needs, if your worried ask at the breastfeeding forum, but I don't believe she needs any extra water ofr feeds due to heat. Breastmilk provids all of that. Get her down for her naps 10-15 minutes sooner then you do now, and keep doing it sooner untill you find the right time for your DD. Start using Pat/Shh to calm your LO before naps, she's old enough now that you can also try PU/PD. Stick with pat/shh to start, then when she is calm lay her down, when she cries pick her up and repeat. This is a slow process, I wont lie, there is a lot of crying. Your DD will be thinking "no mum this is not how we go to sleep" your aim is to guide her and to teach her a new way to fall asleep. To show her she is safe to sleep. Avoid rocking to sleep. You'll want to have 2 naps of 1.5 hours, and one 45 minute cat nap.
Bedtime needs to be changed. Earlier is better for LO's. Contrary to what many think, keeping your LO up later doesn't make them sleep longer, it only makes them overtired and tends to make them wake more. Move bedtime to 7pm and make sure your last nap is at least an hour earlier. The last nap before bed is usually the cat nap.
For the reflux do you have the crib matress at an angle? if not that may be your problem, many LO's with reflux can't lay flat. Try elivating the matress or somthing if you can. Ask at the reflux and colic bored for more advice on making your LO more comfortable. I know the matress thing worked for us though.
Also remember there is a difference between a mantra cry and a real cry. Listen to your LO very carefully, its different for each LO, but if you listen you can spot the difference. My DD's is very flat, doesn't get lowder and starts and stops for example when its a mantra cry. If you believe its a mantra cry then by all means give her a chance to settle, if its a real cry then go to her. It takes time but you'll figure it out. Its just really hard to explain.