SV...I forget where in Texas you are, but I use tap water up here in Fort Worth and have noticed very little difference in the plants using rain water or using tap water...I usually let the tap water stand overnight before using to let the excess chlorine come off...but sometimes when I am watering/feeding, I will use it right away...
get you a small water test kit and check the pH of your water...if it is too alkaline, that could be the reason for your peppers yellowing...once the ph of your soil gets above 7, the soluability of the different elements the plants need is reduced....here ia a link to a pretty good article that gives a better explanation and two of the items your plants really need, Calcium and Magnesium start decreasing at 7.....you can have all the nutrients required for plant growth in the soil and if the ph is off, you are beating a dead horse...they just won't ionize...
http://www.extension.org/pages/Soil_pH_and_Nutrient_Availability
everyone has their own way of doing things, but my plants start getting fed about a week after they sprout...I feed them 1/2 strength Botanicare products...then when they get transplanted to 3" containers (about three weeks for annuums and 4-5 weeks for chinense), they get full strength...
IMO you definitely have a nutrient deficiency/balance issue...your best friend is epsom salt foliar feed (1 Tbsp per gallon of water) - this provides the required magnesium directly to the leaves and can be absorbed thru the stomata...as far as nitrogen goes...
bottom line IMO, the plants look like they are starving to me...give them a shot of nitrogen along with the epsom salt foliar feed and see if they don't change their look in a week...
are those Jalapenos?