Don't over stress.... give it a chance to adapt to its new environment.

You're over-watering and/or there is a high level of dissolved solids (salt, from tapwater and fertilizer solution) in the soil (solution). Also, dracaena doesn't do well with fluoridated water, and fluoride is accumulative in plant tissues. It's best to water with some form of deionized water - distilled water, rain, snow melt, dehumidifier or air conditioner condensate, and water from a reverse osmosis filtration system are all good sources. I can see water which exits the drain hole is allowed to sit in the collection saucer, providing a pathway by which all the salts flushed from the soil are able to reenter the soil. Your pot should sit above the effluent that collects in the saucer.It looks like it might be in the original pot, if so, it undoubtedly needs repotting for one of 2 reasons - root congestion (rootbound) or the soil might have collapsed and you're dealing with root rot. There are many recommendations I could make, but I think you would benefit from reading the link I'll leave. It will also help you ask the right questions. Follow me to what Al is talking about. Al

Since we don't really know the growing conditions, it is hard to speculate on what is the problem (if any). I would suggest that instead of watering on a weekly schedule, water only when you need to. And that will be determined by the potting media and indoor conditions. I have copied Al's (tapla) great instructions for using a "tell" to determine when to water. By far the best method to judge watering needs if not very familiar with both the plant and the media. "Start using a 'tell' to 'tell' you when it's time to water and things will probably straighten out. It won't be over-night, but you should start to see a difference right away. Using a 'tell' Over-watering saps vitality and is one of the most common plant assassins, so learning to avoid it is worth the small effort. Plants make and store their own energy source – photosynthate - (sugar/glucose). Functioning roots need energy to drive their metabolic processes, and in order to get it, they use oxygen to burn (oxidize) their food. From this, we can see that terrestrial plants need plenty of air (oxygen) in the soil to drive root function. Many off-the-shelf soils hold too much water and not enough air to support the kind of root health most growers would like to see; and, a healthy root system is a prerequisite to a healthy plant. Watering in small sips leads to avoid over-watering leads to a residual build-up of dissolved solids (salts) in the soil from tapwater and fertilizer solutions, which limits a plant's ability to absorb water – so watering in sips simply moves us to the other horn of a dilemma. It creates another problem that requires resolution. Better, would be to simply adopt a soil that drains well enough to allow watering to beyond the saturation point, so we're flushing the soil of accumulating dissolved solids whenever we water; this, w/o the plant being forced to pay a tax in the form of reduced vitality, due to prolong periods of soil saturation. Sometimes, though, that's not a course we can immediately steer, which makes controlling how often we water a very important factor. In many cases, we can judge whether or not a planting needs watering by hefting the pot. This is especially true if the pot is made from light material, like plastic, but doesn't work (as) well when the pot is made from heavier material, like clay, or when the size/weight of the pot precludes grabbing it with one hand to judge its weight and gauge the need for water. Fingers stuck an inch or two into the soil work ok for shallow pots, but not for deep pots. Deep pots might have 3 or more inches of soil that feels totally dry, while the lower several inches of the soil is 100% saturated. Obviously, the lack of oxygen in the root zone situation can wreak havoc with root health and cause the loss of a very notable measure of your plant's potential. Inexpensive watering meters don't even measure moisture levels, they measure electrical conductivity. Clean the tip and insert it into a cup of distilled water and witness the fact it reads 'DRY'. One of the most reliable methods of checking a planting's need for water is using a 'tell'. You can use a bamboo skewer in a pinch, but a wooden dowel rod of about 5/16” (75-85mm) would work better. They usually come 48” (120cm) long and can usually be cut in half and serve as a pair. Sharpen all 4 ends in a pencil sharpener and slightly blunt the tip so it's about the diameter of the head on a straight pin. Push the wooden tell deep into the soil. Don't worry, it won't harm the root system. If the plant is quite root-bound, you might need to try several places until you find one where you can push it all the way to the pot's bottom. Leave it a few seconds, then withdraw it and inspect the tip for moisture. For most plantings, withhold water until the tell comes out dry or nearly so. If you see signs of wilting, adjust the interval between waterings so drought stress isn't a recurring issue."

If it doesn't perk up or it starts looking worse, then cut it back hard. Keep on watering as needed. The problem is almost never fatal but you may or may not see any clean regrowth this season. Even if you do not, it will very likely resume growth next spring as if nothing had happened.