Good Morning and welcome! I am Dr. Loretta, a licensed veterinarian and I am happy to answer your question.
You are correct...this does sound like a "choke" and the treatment for this is a dose of an anesthesia to keep Jake's head down . This way , the fluids produced in the esophagus will saturate the bolus of hay that is stuck. This can take awhile so contacting your vet if Jake will not keep his head down is important because this is a critical to dissolving this mass. Some may attempt to pass a stomach tube but in my experience, this can cause serious damage to the esophageal wall and this you will want to avoid.
Give this time to resolve itself. If it does not, then further treatments such as IV fluids and possible addiction of mineral oil via stomach tube only to where the mass is blocking the esophagus sometimes can add the lubrication so the mass will resolve.
In serious cases, these have been removed surgically but at Jake's age, this is risky.
Does that make sense to you?
Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please REPLY so I can clarify for you.
Sincerely, ***** *****