The success of the Battle of San Jacinto didn’t make life easier for the Texians. Though the Republic of Texas was formally recognized by many countries, including the United States, Mexico continued to send troops into Texas, attacking at every opportunity. Mexico knew it had lost the battle, but refused to believe it had lost the war, too.
General Sam Houston, after treatment for his battle wounds in Louisiana, returned to Texas to be sworn in as the first President of the Republic in December of 1836. Mirabeau B. Lamar, who distinguished himself at the Battle of San Jacinto, became the second President of the Republic December 10, 1839.
During the years that followed the battle at San Jacinto, the government and the army of the Republic would change with Houston and Lamar often butting heads, disagreeing on the direction of the Republic and the military.
The Republic of Texas developed a sizable army and built its own navy, working to maintain independence. The ever increasing army required more and more resources and the cash was dwindling quickly. Nine years of continued battles with the Mexican armies led Texas to fall into near bankruptcy so in 1845, the Republic of Texas sought to enter the United States.
Entering the United States December 29, 1845 as the 28th state brought the United States into the battle with Mexico. Mexico considered this annexation of the Republic of Texas by the United States an act of war. Hostilities escalated when President Polk ordered Gen. Zachary Taylor to Corpus Christi in January, 1846. The Mexican government considered this an act of aggression, so they attacked the American troops stationed at Corpus Christi. The led to the official declaration of war by the United States on May 13, 1846, and the beginning of the Mexican-American war.
March of 1847 saw the United States invading Mexico and by September 14th, the U.S. controlled Mexico City. A peace agreement was orchestrated in February of 1848, giving the United States California, Arizona, New Mexico and the Rio Grande boundary for Texas. Also portions of Utah, Nevada, and Colorado were included in the treaty.
Much is written on this subject, and for those that want to explore more, here are a few reference sites.