1st off, it may be in shock from two things, one a new environment, and # 2 transplanting it. I never transplant a plant for at least 3 weeks after I bring one home. Plants need to become adjusted to their new surroundings ( humidity levels, temperatures, light, and how they are cared for. ) That way they can tolerate they transplanting better.
2nd palms take TONS of light inside a house. Is it getting enough light?
3rd Watering, palms are used to sandy well drained soils. Don't be afraid to water it, but just let it dry a little between waterings, as the roots need oxygen as well as moisture. This is a good rule of thumb for almost all plants.
4th Did you use any fertilizer within 2 weeks of transplanting? That is a very common mistake. The freshly torn roots of a transplanted plant send out new growth rapidly. If they come in contact with the salts in the fertilizer however they can be cauterized, and develop a callous at the tip. Slowing down the regeneration of the roots, also impairing it from absorbing water.
5th. It may have a fungi disease called leaf spot. You should go back to where you purchased the plant and find out exactly what type it is, then do a little research to see if they are prone to that disease, and what type of action you should take.

Hope this helps.

Palms are not variegated (green with white stripes), so it is unlikely that you have a palm. Based on the information you provided, my educated guess is that you may have a Dracaena (Pleomele reflexa or Warneckei, perhaps) or possibly a Pandanus. These plants have a palm-like appearance, but are not palms and have very different cultural requirements.