No, the Texas and Mexican War is correctly known as the Texas Revolution or the War for Texas Indepence and the Mexican-American war began in 1846 ten years after Texas won its Indepence at the Battle of San Jacinto in 1836.
The Mexican American War was declared on 13 May 1846 or on it was April 25, 1846 that the American-Mexican war started as the result of border incident known as the Thornton Affair. The Mexican American war began on 25 April 1846.
The Mexican, or its other name, the Mexican-US War, was in 1846. There is no direct connection to the US Civil War, other then that many of the generals of the Civil War, fought together and came to know each other.