Around this time of year this looks common. Has this plant been out of doors over night? This looks like freeze damage based on this one picture. Please send other pictures and think about what changed just recently.
I also see possible white fly on your plant, not at all a huge problem. What have you used for fertilizer, how much and how long ago?
Water only when the pot and soil and plant feel light to lift. Feel what the weight is like right after watering. 8 pounds per gallon...you'll always know when to water and when not to water using this method. The plant and pot and soil are remarkably light when the plant needs water. Then soak it and do not water again until that potted pepper is obviously lighter than when watered.
Does the plant look like this? Just the tips and exposed leaves are browning or damaged like this? Is the rest of the plant normal, healthy?
A few more pictures, please. Thank you.
Your plants at the size I am seeing need a treatment of NEEM. Fill a 5 gallon bucket 4/5th full and add the amount of Neem on the directions to the water. Take your plant and holding your hand over the soil turn it upside down and SWISH and couple of times in the solution, shake and replace to it's normal spot. Sprinkle some of the Neem solution on top of the soil.
Check your other plants for white fly and/or spider mite (usually happens atst). If small plants that you can dunk, go ahead and use the same solution, Swish Swish, Shake and put back in their normal spot. If you decide to spray Neem, do it at night and take your plant out of doors to spray. Do this even if you dunk. Neem is stinky and I am not assured that Neem doesn't hurt bees, butterflies and beneficial insects. Wear gloves and long sleeves. Even though Neem is considered Organic, and it is, this should show you the power of chemistry in the natural world. Organics are some of the most toxic substances we know and use.
Clean the surfaces of the furniture and floor and carpet and window sills.
Allowing plant leaves to touch the windows when it is freezing outside will cause this as well. Even when it is really hot outside, this can damage the epidermis of plants.
Note: If there is white fly I don't think that white fly is the cause of the tips. Do take off the peppers before dunking or spraying with Neem. Try to not spray the flowers if possible. Use a magnifying glass and look beneath the leaves and on stems as well and tell me what you find. Perhaps I just need to clean my glasses? Otherwise I think you might have over fertilized? What is the formulation?