If you succeeded in stopping the Mexican attack, there would be no shouting of "Remember the Alamo!" in the future. Maybe without the tragic loss of the Alamo defenders and the cherished memory of their brave sacrifice, there's not enough motivation for the rest of the Texian forces to finally defeat Santa Ana? And you only brought 75 lbs of gear with you - enough to fight one battle. You expended all, or nearly all of your 5.56 ammo at the Alamo by judiciously killing every single Mexican soldier with one well-placed shot. There is no possibility of resupply.
Your AR15 is now a dead weight, useless for any further defense of the Texian cause, and so you wisely decide to hide it to keep it from falling into the Mexican victors' hands. Texas eventually enters the Union by US conquest instead of as the result of the 1844 annexation by treaty, and the independent Texan spirit dies out.....making Texas just like any of the other sheeple-states. You die a couple of decades later of old age ......or of some simple disease, easily curable today with antibiotics....which don't exist in the first half of the 19th century. Someone eventually discovers your hidden AR15 just in time for the outbreak of hostilities in the War of Northern Aggression. But while they can figure out that this is the "mysterious rifle that saved the Alamo", nobody can figure out its function.......your plastic PMAGs having been thrown away by your survivors, since nobody knew what they were for. There are no unfired cartridges for it so nobody can test its single-fire function, and even your spent cases from the Alamo battle are long gone.
Texan General John Bell Hood takes possession of the rifle upon its discover, as a perhaps useful artifact to be studied by the Confederacy in future years, and has it forwarded to the gov't archives in Richmond. There, it languishes in its crate until the capture of Richmond in April of 1865, and Secretary of War Stanton has the entire confederate archives transferred to DC for future study. There being no useful reason for the Union to allow a thorough knowledge of the motives of the confederate leadership to be disseminated to the people, the entire confederate archive is transferred to the same Double Super Top Secret gov't warehouse which, 80 years later, will house the Ark of the Covenant captured from the nazis on a mediterranean island. Your AR15 will be housed in the same section of unexplainable phenomena, and dour-faced top secret archivists will conclude that aliens must have, albeit unsuccessfully, aided the Confederacy.
Your AR15 languishes in unknown obscurity until 1954, when a young firearms designer with Double Super Top Secret clearance by the name of Eugene Stoner, browses the hidden archive looking for anything unusual in weaponry that might inspire or inform the idea he has in his head for a new self-loading rifle that his employer - Armalite - has tasked him with designing. He finds your AR15, and instinctively understands its workings.....except he can't figure out why it is chambered in a "poodle-shooter" caliber. He realizes that scaling it up to take the mighty .30-06 Springfield cartridge would defeat some of the advantages of the rifle due to overall cartridge length. Hearing of research into the T-65 .30 caliber cartridge being considered as a replacement, he designs the "new" rifle around the T-44 cartridge which becomes the 7.62NATO cartridge......and the AR10 is born. But it is too late .....the Mighty M14 has won acceptance with the Dept of Defense.
Under pressure from the aptly-named then-Secretary of Defense Robert Strange McNamara, Eugene Stoner's staff engineers take his AR10 design and scale it down for a new "poodle shooter" cartridge - the .223 Remington - which when modified slightly to mil-spec needs, becomes the 5.56 NATO. The M16 rifle is accepted into service in 1964, and the civilian AR15 rifle begins civilian sales.
SIX DECADES LATER, you purchase an AR15. You devise a plan to build a time machine and return to 1836 Texas with your AR15 carbine, 8 full 30 round magazines, and approximately 1500 rounds of 5.56 NATO ammo, to try and turn the tide of the Battle of the Alamo. You succeed in going back in time........ the circle repeats, proving that the AR15 rifle system is, always was, and evermore shall be - independent of any human intervention - a free-standing wonder of the world, unrecognized as such by anyone who doesn't have one. The fallacy that Eugene Stoner designed it is allowed to be propagated by the fedgov't, because the Double Super Top Secret gov't archivists' secret in the Alien Artifacts section of the secret gov't archive have concluded that the American public is ready for The Truth........that we are not alone.
I don't believe in time machine exercises as anything more than an observer.