My first thought is...it's too wet.
That plant definitely has a problem (or problems).
I'm a newbie VFT grower so take my comments with a grain of salt or your favorite seasoning.
VFT plants are rather robust plants *if* given the correct growing conditions. Miss one condition and apparently they are unforgiving and decline in health...sometimes rapidly.
Apparently the plant was healthy when you bought it and you quickly repotted it into a larger pot. Correct?
The growing medium that you are using looks to be peat moss. I see no sign of sand or perlite mixed with it but sometimes that can be difficult to see in photos (especially the sand). What does your medium consist of? Did you rinse your grow mix well before transplanting?
I agree with Dean...they do best under the sun. You may need to ease them into full sunshine gradually, though. I threw my little typical flytraps out in the sun after only a few days of acclimating to full sun after being in the shadows of the store I bought them from. They struggled for several weeks but are growing nicely now in full, hot sun.
Your water sounds good (distilled) as long as it truly is pure distilled water. A TDS meter runs around $15 on Amazon here in the USA...it is a very good tool to have to keep a check on water quality.
As I mentioned at the beginning...the growing medium looks rather wet and I see water in the bottom of the tray which goes along with your statement regarding using the tray method. I would say that if you are continuously keeping water in the tray and the soil stays as moist as it appears (if the photo depicts the normal state of affairs) then you are keeping your plant too wet. Flytraps want moist soil, not constantly soggy soil. If the plants are outdoors in hot sun and temperatures in the 90's and a drying wind it is good to keep water in the trays as evaporation and transpiration will cause the water to be used or lost fairly quickly. But, inside with 90F and 50% humidity, keeping the plants constantly standing in water may be drowning them or at a minimum causing unhealthy conditions. With my few little flytraps sitting outdoors in the hot south Alabama sun I tend to let the surface layer dry out a bit between waterings. I often use the tray method during some of the hotter times but I still let the tray go dry for a day or two or three. When I let the tray go dry the pots still feels heavy with moisture when I lift them but letting the tray go dry helps dry out the upper level of the growing medium...and the pots gradually get lighter in weight. When it's down in the 80's I usually just top water and go by how "heavy" the pot feels to me. I don't let the pots dry out to where they feel too "light"...there's a short learning-curve to learning the "weight" gauging but it's easy to catch onto. VTFs don't need to be standing in water all of the time, especially indoors (but get them outside under the sun if you can!).
Again, I'm a new grower and these are my thoughts from my experiences and from reading *way* to much info on the Internet! I'm a bit OCD about researching things that I get interested in.
Best wishes to you and your plants and welcome to the forum!