This is an unusual and beautiful sword, and could well be one-of-a-kind according the engraving on the blade.
It's certainly US military (the 13-star circlet attests to that), it's also an officer's dress sword, and it dates stylistically to circa 1812 - 1826. However, which branch of the military it belongs to is unclear, but it could well be an early example of a US Marine Corps officer's sword. The markings on the blade are very similar to those of a US Naval officer's sword of the day, but instead of a fouled anchor insignia (US Navy) yours has an "eagle, addorsed and rising from a globe" (in heraldry parlance) which is all but the same as the Marines' insignia but without the anchor. If it's an early variant of the Marines' eagle & globe, it's an extremely rare one.
The star on the scabbard is also unusual, it's too early to have anything to do with Texas because it was part of Spain, and later Mexico, during the period this sword dates to. It may just be ornamental as it's a repeat of the star on the crossguard, which would be a conceit of the maker rather than the military engraver.
The sword itself is very likely English made, which was not unusual as US manufacturers did not have the expertise or technology to fabricate a sword like this in those days and almost all were imported from mainly England (Sheffield steel) and Prussia (Solingen steel) and the blades usually custom-engraved/etched in New York or Philadelphia.
The design and ornament of the sword itself is completely pleasing, made with its stylish eagle head pommel (so popular at the time with US officers) enclosing a carved ivory grip, the recurved knuckle bow with clasping foliate forms joining an elaborately embellished quillon with acorn tips. The blade blued and damascened with a 13-star circlet flanked by the eagle-and-globe on one side and a "panoply of arms" on the other.
It has its original gilt metal scabbard, with some wear and fading to the gilding, original gilt hanger mounts and bands and 'drag' on the chape (scabbard tip) engraved with vining oak leaves at each end and a central five pointed star in a circle.
So what about value? The top auction price for a US officer's dress sword from this period that I can find in the records is this example, a US Naval officer's sword, very similar to yours, but with a leather scabbard and in extremely fine condition, even better condition than yours. It sold on line for $9,500.
Having said that, yours is also a museum piece. Conservatively it would have an auction value in the range of $3000 - $5000 and I would therefore insure it for at least $10,000.
I do hope this helps!
Please let me know if I can be of further assistance with this, I would be glad to.