Hi Lilly,
Yes, you should increase your calories if you want to maintain your weight. The on-line calories for the Cycle Diet is any where from 1,600-1,800 kcals...very short from where you need to be. You are currently underweight if I calculated your kilos correctly to pounds for your height. 6'1". You should shoot for 65 kilos or 144 pounds. Just to maintain your current weight you need to be at 2,024 kcals so I agree you need to be up to 2,500-3,000 kcals, especially if you exercise.
Lilly, have you ever been tested for Celiac Disease? You describe the classic signs of Celiac....always eating a ton of food but not able to gain weight. Please talk with your doctors for a blood screening. They will more than likely want to do an endoscopy as well.
Are you trying the gluten-free diet? Please get yourself tested for celiac first before you go gluten-free....but as soon as you get tested you can go gluten-free. If you are trying the gluten-free diet you will have terrible gluten grain cravings due to the addictive nature of gluten. Gluten is a tough little molecule to kick

but you can do it if you have to.
Substitute some non glutenous grains like:
Beans
quinoa
*buckwheat
*groats
*wild rice
*brown rice
**Pure oats
*sorghum
*millet
*tapioca
*corn
*Montina
*Teff
Eat enough to satisfy your hunger, you should increase your calories to maintain your weight.
Lilly, many times gluten can cause a psychiatric or neurological disorder so it's very important you get tested as soon as possible.
And yes, the Cycle Diet is a good diet for you but you need to be on the right diet for you if you have a gluten intolerance.