Learn English – Does “Hang a Shingle” refer only to lawyers starting their own business

No, it's not restricted to lawyers:

hang out one's shingle
Open an office, especially a professional practice, as in Bill's renting that office and hanging out his shingle next month. This American colloquialism dates from the first half of the 1800s, when at first lawyers, and later also doctors and business concerns, used shingles for signboards.

[The American Heritage Dictionary of Idioms by Christine Ammer. S.v. "hang out one's shingle." Retrieved February 8 2016 from http://idioms.thefreedictionary.com/hang+out+one%27s+shingle ]

With respect to the etymology of the phrase, the earliest use I could find with reference to 'hang a shingle' was this from a letter dated January 20, 1830, in The Constellation (also known as the New York Constellation and the Constellation Advertiser), subsequently picked up and republished in the Indiana Palladium, 9 April 1831:

Dear Tim, In my last letter, I told you I'de managed to keep out of jail, tho' one feller tried plaga hard to put me in. I guess I was a lawer enuff to cast him twice, tho' he was a lawer too and a pretty slippery one into the bargin. The first time he spelt my name in the writ Timbletoes, and I upset him there, cause it was no name of mine. The next time he want on the spot and the justas faulted him--so you see I've half a mind to stick up a shingle as turney at law, if there want so plagy many of them here already--they're as thick as flies round a bunghole.

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An earlier published instance with reference to writing on a shingle was the following in The Genius of Liberty, 21 February 1829 (Leesburg, Virginia), which was also picked up from a New York paper (unnamed):

Anti-Tariff Bagging.—On board the ship Othello, from Charleston, one of the bales of cotton has a wrapper of what is termed “anti-tariff bagging,” which we understand is manufactured from white-oak splits, we are told also that it was accompanied with a letter of advice written on a shingle! —[N. York paper

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A somewhat later publication describing writing on a shingle was this (again) from The Genius of Liberty, 17 November 1832:

The Yankees knew the way to the West Indies a good while ago; they knew more ways than one.—Their coasting vessels knew the way, without quadrant or Practical Navigator. Their skippers kept their reckoning with chalk, on a shingle, which they stowed away in the binnacle; and by way of observation, they held up a hand to the sun.—When they got him over four fingers, they knew they were straight for the Hole-in-the-wall; three fingers gave them their course to the Double-headed-shot-keys, and two carried them down to Barbadoes.

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Then, in another, later edition of The Genius of Liberty (28 February 1835), this note can be observed:

The editor of an anti-masonic paper at Harrisburg, Pa. having been expelled his seat in the house of representatives of that state, as reporter, is now taking notes on a shingle, it is said, in one of the galleries.

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All together, these occurrences referring to writing on shingles as signage on a bale of cotton (1829), a "lawer's" place-of-business advertisement (1830), and a handy 'slate' for making notes (1832, 1835) tempt the conclusion that shingles were a cheap and ready substitute for more conventional writing surfaces in the early 1800s. The practice of lawyers using shingles to advertise their workplaces was the natural outgrowth of shingles' broader, more general application as signage and 'writing slate'.

Thus, it would be justifiable to suppose that shingles were, early on, used for signage at places of business, regardless of the type of business. To 'hang out a shingle' was equivalent to 'placing a sign'. Additionally, instances of the phrase in early publications invariably specified the exact use of the shingle or, if a place of business was so announced, the type of business that employed the shingle. This broad use of the phrase is further documented in Sven's most excellent answer, with published instances from 1834, 1839, 1843 and 1845.