I do not know the source of that claim. I can tell you it was not widely held. There were several debates and controversies about the extension of railroads. I haven't seen any claims of boiling blood or suffocation. Notably, it's totally absent from the records of the House of Lords and House of Commons. Since Parliament needed to sanction most new lines, this means that no railroad opponent ever decided to put the theory before decision makers.
It's understandable why. It would be a strange, easily disprovable objection. The first railroads came about in the late 18th century. The technology was originally used to transport goods and had been ridden before. For example, one line moved coal from a mine to a city, and the miners sometimes hitched a ride. But these lines did not have much of an impact on the public consciousness. The public largely didn't travel along them. For example, public railways had been around for about two decades by Jane Austen's time, yet she makes no mention of them. By the time passenger railroads were beginning to crisscross the country, workers and conductors had been riding them for decades.
Objections to railroads tended to coalesce around four (and later five) points:
1.) Railroads caused pollution. (This is the main one where health concerns came in.)
2.) Railroads decreased property values where they passed through, by pollution and being ugly.
3.) Romantic sentimentalism, along the lines of 'railroads are unnatural' or 'God did not intend man to go so fast'.
4.) Objections to the destruction of specific sites, objects, or town layouts to make way for a railroad.
5.) Later on, as railroads became big companies, anti-corporate arguments about the abuses of the companies themselves.
There were two medical effects that caused much ink to be spilled: railway spine and inhaling the fouled air. Railway spine is today called whiplash. The fouled air is called smog. Both are very real, though the dangers were often overstated by opponents. For example, a town in Northampton protested the passing railroad would turn their sheep's wool black. But they're not as salacious as claims about boiling blood or suffocation.
Sources:
To add to this question, I've also read that it was commonly believed that going more than 30 mph would boil humans blood. Was that commonly believed as well?
I believe there was also a belief, or maybe cultural fear would be a better term, that railways could cause madness. Not necessarily anything that would have been raised as a more official objection, but it appeared here and there in newspaper stories and novels.
Source: "Shattered Minds: Madmen on the Railways, 1860-1880," Journal of Victorian Culture 21:1 (2016): 21-39.
Were 19th century ice boats able to go faster than 30 mph, and if so was that well known?