For Splenda, 3 packets or less is 0 points and 4 packets are 1 point. That's according to the weight watchers online points tracker. For equal, it takes 6 packets for 1 point.
It might take you some time, but probably try to 'wean' yourself off that much. Tuvia is natural and probably much better than the Spenda or Nutrisweet. Look at the ingredients in those....can do all kinds of things to a person. Might be why you feel terrible. Plain water is a good thing for many reasons. Hope you try to cut back, bet you will see a difference in how you feel.
A couple of products that I've found are good to use with water.
True lemon -- this is simply crystallized lemon. It gives water a nice flavor (or tea) and adds no calories. I freely use this.
True Lemonade -- 10 calories if you use the whole packet for 16 ounces, This does use a little evaporated cane juice and rebiana (made from Stevia).
I really wanted to get away from aspartame and some of the other artificial sweeteners and found this was best for being low calorie and not having artifical sweeteners in it. A packet of True Lemonade is really enough for 16 oz. water so you might want to try it for a lower calorie alternative (crystal light has a similar product but it is higher in calorie). Sometimes I even use half a packet of the True Lemonade. There is also a Raspberry Lemonade by the same company that is good.
I don't usually count the True Lemonade if I have one or two packets in a day. If more I will count a point.