Optimal drip irrigation management in shallow groundwater areas needs to clarify the effects of flow rate and layout designs on the soil moisture, salt distribution, cotton root length density, plant height, leaf area, and yield. In this study, a one-year field experiment was conducted from April to October 2018 in the fifth company of the 16th Regiment in Alar City, Xinjiang, to investigate the effects of various drip flow rates and layout designs of cotton growth. Two drip flow rates (2.8 and 5.6 L·h−1) and two layout designs (one film, two drip tapes, and six rows; one film, three drip tapes, and six rows) were applied to explore the optimal combination, resulting in a total of four treatments that were irrigated three times in the whole growth period. Soil moisture, salt distribution, cotton root length density, plant height, and leaf area were measured. The main results were as follows: (1) Under the same layout designs, the soil moisture content was higher and the soil salinity was lower when the drip flow rate was 5.6 L·h−1, and the cotton root length density, plant height, leaf area, and yield were significantly higher than that of 2.8 L·h−1. (2) Under the same drip flow rate, the soil desalination rate, cotton growth indexes, and yield under the three-tapes treatment were significantly higher than the values of the two-tapes treatment. The actual yield of treatment D was 21.56%, 19.23%, and 11.71% higher than that of treatments A, B, and C, respectively. (3) The crop evapotranspiration of cotton during the two irrigation cycles showed an increasing trend, and the groundwater contribution showed a smaller and then increasing trend. Overall, the combination of three tapes and a drip flow rate of 5.6 L·h−1 had the highest cotton yield and net income, which were 6211.36 kg·hm−2 and 4820.21 kg·hm−2 for the theoretical and actual yields. The results of this study can provide a reference for the management of limited irrigation leaching soil salinity and cotton cultivation in shallow groundwater areas.