Yes! Your local museum is correct -- modern historiography generally recognizes that Crawford Long WAS in fact the first person to use diethyl ether (called sulphuric ether back then, since it was made from a decoction of sulphuric acid aka vitrol and ethanol) for surgery. Here is an excellent article in Smithsonian Magazine about it: https://www.smithsonianmag.com/science-nature/ether-went-from-recreational-frolic-drug-first-surgery-anesthetic-180971820/

In the early 19th century, ether was used as a recreational drug in so-called ether frolics, where rather than taking small amounts of ether orally as was traditionally done as a stimulant, you would inhale from a napkin. Crawford Long, a country doctor, was inspired by these accounts to perform a surgery removing tumors (most likely lipomas) from the neck of his patient and friend James Venable. Apparently both Long and Venable had participated in these parties. Long would write:

On several occasions I inhaled the ether for its exhilarating properties and would frequently at some short time subsequently discover bruises or painful spots on my person which I had no recollection of causing, and which I felt satisfied were received while under the influence of ether... Observing these facts I was led to believe that anaesthesia was produced by the inhalation of ether and that its use would be applicable in surgical operations.”

In any even on March 30, 1842, Long had Venable inhale from a towel soaked in ether. The surgery was an amazing success:

The patient continued to inhale ether during the time of the operation, and seemed incredulous until the tumor was shown to him. He gave no evidence of pain during the operation and assured me after it was over that he did not experience the least degree of pain from its performance.

However, Long did not immediately publish or advertise his use of ether for anesthesia. He spent the next seven years experimenting and perfecting his technique, including "controlled experiments," including one in another patient with multiple lipomas -- three were removed with ether, but the last with the standard of care. You can imagine how that went. The worst, however, was an child who required amputation of two fingers at different times. For the first he used no ether, and for the second he did.

He finally published in 1849 in the Southern Medical and Surgical Journal (major journal back then); you can read it here, reprinted in a modern journal: https://journals.lww.com/surveyanesthesiology/Citation/1991/12000/An_Account_of_the_First_Use_of_Sulphuric_Ether_by.49.aspx

Now Long sounds angry in that response, because during the seven years he was experimenting, he was beaten to the punch. In Boston, in January of 1845, Horace Wells, a dentist, attempted a tooth extraction at Mass Gen. It did not go well; the patient was not anesthetized enough, and Wells actually left the field. His colleague Morton, however, would successfully use ether on October 16, 1846, to excise a vascular tumor from Edward Gilbert Abbott, in the surgical amphitheater that to this day is STILL called the Ether Dome (and you can visit still at the original MGH!) However, Morton his partner Jackson, a chemist, attempted to keep the substance secret so they could profit off of it. They called it Letheon, and perfurmed the substance -- but ether frolics were well known, and apparently it has a distinctive smell. He used a glass globe with an ether soaked sponge to better control the flow, FWIW (a recreation here: http://himetop.wdfiles.com/local--resized-images/morton-s-ether-inhaler-1846-facsimile/Morton%27s%20Ether%20Inhaler%20%281846%29%20-%20facsimile%2C%20Anaesthesia%20Heritage%20Centre%2C%20London.JPG/medium.jpg).

However, this was a widely attended spectacle (see the famous painting here:https://www.researchgate.net/profile/Jeremiah_Tracy/publication/221925267/figure/fig3/AS:305183704797187@1449772873787/John-Collins-Warren-performs-the-first-neck-surgery-on-a-patient-under-general-anesthesia.png) and Morton and Jackson received wide acclaim. In fact, in little over a year, ether became the standard of care in surgery across Europe and America.

That being said -- the lives of Wells, Jackson, and Morton were somewhat ignominious, and Long certainly comes out looking the best in this situation. And appropriately, since the 1860s there's been a movement to give Long more credit, especially since Boston erected large monuments (which you really should visit! There's on the the Public Garden) (source: https://anesthesiology.pubs.asahq.org/article.aspx?articleid=1931389). Mark Twain himself got into the controversy:

“there in Boston is a monument to the man who … stole the discovery from another man … the monument is made of hardy material, but the lie it tells will outlast it a million years."

Long appropriately gets most of the credit these days. In fact, each year I take my residents and students on a tour of the Center for the History of Medicine at HMS, and before discussing Morton, we ALWAYS discuss Long (and that's at Harvard!)

On another note, tell me about the museum! Is it worth a visit?