Of American-English origin, the phrase a frog in one’s throat, also a frog in the throat, designates an irritation in the throat suggestive of an obstruction, producing a temporary croakiness or hoarseness.

The metaphor of a frog in one’s throat has occasionally been associated with the French.—In this regard, cf., below:
– quotation 1 from the New-York Evening Post (New York City, New York, USA) of Tuesday 8^th March 1808;
– quotation 5 from The Madisonian (Washington, District of Columbia, USA) of Saturday 14^th May 1842.

The metaphor of a frog in one’s throat was also associated with the French in the following from a transcript of the remarks that Mr. De Courcy made on the currency resolutions introduced into the Senate of Kentucky by Mr. A. K. Woolley—transcript published in The Frankfort Argus (Frankfort, Kentucky, USA) of Friday 2^nd February 1838 [Vol. 2, No. 4, page 2, column 1]:

The 11^th Resolution puts me in mind of the story of the Frenchmen [sic] who was swallowing little frogs, a person standing by observed he made sundry wry faces; asked the reason. Reason enough he exclaimed. In my hurry I got hold of the wrong end of the animal and swallowed it tail foremost, and in its descent into my stomach it scratched a little. Were I to attempt to swallow this Resolution Mr. Speaker, I am certain it would not only scratch but stick, and in that case I should be doomed to drag out a pitable [sic] existence with a frog in my throat.

The association of the metaphor of a frog in one’s throat with the French probably alludes to the fact that the noun frog (which has long been a general term of abuse) is specifically applied to the French.—Cf. origin of ‘Froggy’ (French).

The earliest occurrences that I have found of the phrase a frog in one’s throat, also a frog in the throat, used in relation to croakiness or hoarseness, are as follows, in chronological order:

1-: From the New-York Evening Post (New York City, New York, USA) of Tuesday 8^th March 1808 [No. 1,952, page 2, column 4]—reprinted from The Salem Gazette (Salem, Massachusetts, USA) of Friday 26^th February 1808:

WASHINGTON’S BIRTH DAY
Was celebrated on Monday last by the Washington Fire Club in this town, according to their annual custom. […] After dinner a number of appropriate songs were sung, and the following toasts given:
[…]
7. France: When she attempts to “raise her voice” in our councils, may she find a frog in her throat.

2-: From Brief hints to those who need them, by ‘Q.’, dated Washington, District of Columbia, Monday 4^th September 1837, published in the Alexandria Gazette (Alexandria, Virginia, USA) of Wednesday 6^th September 1837 [Vol. 13, No. 4,652, page 3, column 3]—the author explains: “These are pencil notes that I made whilst sitting in the lobby of the House of Representatives”:

Mr. T——s of Md., may be a great man in his own estimation, but loud talking, with a frog in his throat, will never convince others of that fact.

3-: From The Louisville Daily Journal (Louisville, Kentucky, USA) of Friday 19^th July 1839 [Vol. 9, No. 206, page 2, column 2]:

Why does not the editor of the Advertiser boast as loudly now as he did last winter of the great loco foco gain to be achieved in the approaching Legislative elections of this State? What is it, that has suddenly brought his frog up into his throat?

4-: From The National Gazette (Philadelphia, Pennsylvania, USA) of Friday 22^nd October 1841 [Vol. 21, page 4, column 2]:

The Concert last night did not pass off with spirit. The weather was gloomy, and the auditory as dull as could be desired. Mrs. Sutton was in capital voice, and did her part with her accustomed care and earnestness. But, from the first note it appeared that Signor Antognini had a colony of frogs in his throat; his singing, which excited enthusiasm on his first appearance, fell flat and spiritless on the ear during three pieces; and in place of a fourth, came an apology, that a severe cold under which he was laboring, incapacitated him from going on.

5-: From The Madisonian (Washington, District of Columbia, USA) of Saturday 14^th May 1842 [Vol. 5, No. 141, page 4, column 3]—reprinted from the Pennsylvanian:

We must insist upon it that bleak and barefaced winter or the glowing, mature summer, is more safely to be trusted than the time of buds and blossoms. We therefore persist in our caution about flannel and damp-expelling fires. A cold in the head or a stitch in the side, is a sad return for sitting on a mossy bank to watch the violet opening its blue eye, it is unpleasant to greet Flora with a sneeze, and though the music of the streams just released from the icy bonds of winter, is sufficiently melodious, yet a ‘frog in one’s throat’ is not a fascinating companion, unless it be taken after the French fashion.