Hello Paisleylighthouse and welcome!
It is certainly possible, though not probable, that you are allergic to your F&P mask. Based on your description, the 'triangle' rash is likely from what is called 'contact dermatitis'. This is not an allergy, but a sensitivity to or irritation from the chemicals used in the manufacture of the mask cushion.
You may be able to go back to using your F&P successfully. Some things you can try:
1. Wash the mask, especially concentrating on the cushion that makes contact with your skin, very vigorously and use lukewarm water. Wash it a dozen or more times, drying the mask completely between each wash. Yes this will take some time and effort but could prove worth it to you. Use unscented baby shampoo or Ivory Liquid (Classic only!) dish detergent. There are a few 'organic' or natural detergents you can use as well. Read the labels and make sure there are no oils or fats in any you use. ("Soap" by definition contains fats and oils, especially coconut.)
2. Try K-Y or other water-soluable lubricant on the part of your mask that contacts your skin. Do not use vaseline, mineral oil, or anything containing oils, fats or petroleum products.
3. Try Mack's Silicone Putty ear plugs and create a 'gasket' on your mask. These are discs of soft, moldable silicone. You can roll out an earplug into a long thin ribbon and apply to the edges of your mask. Thinner is better. This is great for leaky spots too as you can build up a little more silicone putty where you need it. This will lightly stick to your mask and your face, but peels off easily. Many people get several nights from one application.
4. There is a cream sold for people who must wear latex gloves and experience contact dermatitis from the chemicals used in the manufacture of these gloves. It is called "barrier cream", it is a little difficult to come by but is available through medical supply outlets or sometimes a hospital pharmacy. This is a silicone formulation that traps moisture, creating the barrier. Apply to both mask and skin where mask comes in contact.
6. Take a look at the Sleepweaver mask. (Google for Circadiance CPAP mask or Sleepweaver CPAP mask.) This is a cloth nasal mask. It is very comfortable and very quiet. I could not use this mask as my face is very small and the mask is only one size, it's too big for me. They offer a 30-day money back guarantee right on the website, you don't need to go through DME just order. If you have insurance, they have on the website the insurance codes you need to bill your insurance (do check with your insurance first to make sure YOU can bill them without going through DME or doctor. Most/all will do this but check first to be sure.)
If none of these 'tricks' make your F&P mask usable for you, try looking at some of the other nasal cushion masks available. Many DME's will give you a 30 day trial at no cost of a mask, this should be sufficient for you to determine if another manufacturer's mask has chemicals that will bother you.
You might also take a look at the mask I use. It is a full face mask. I don't need a full face mask (I'm not a mouth breather) but I've found this mask to be the most comfortable and quiet of any mask I've tried (nearly a dozen now). It is called the Hans Rudolph Full Face Mask, google for it. It will be called the VIP, VIP 7600, 7600. You can see it at Direct Home Medical for one. There is a picture in the gallery of masks here on this site, too.
It is one piece molded soft silicone, with an optional thin silicone insert for the nose if the nose has leaks. It is a goofy looking mask (!) especially the headgear but it stays put and is very comfortable IMO. There is a newer model called the V2 which is slightly different shape one piece silicone and does not need the nose insert. The V2 headgear is simpler and attaches to the mask a little differently.
I hope this helps. Best of luck to you, blessings,