I've heard people say "she doesn't have a shred of decency." Is it grammatically correct to say "I don't' feel a shred of sleepiness?" I'm in doubt because I am thinking: a shred is a very small piece scraped from something larger. And sleepiness is not an object so technically it can't be a "shred"... Please enlighten me :)
Yes, this is fine to say. "Shred of decency" is a set phrase and is by far the most common thing to have a shred of but anything similar can work.
As you mentioned, "shred" simply means a very small amount.
You can be different amounts of sleepy. It is normal to say "I am not that sleepy" or "I am very sleepy" and sleepiness can be used on this scale as well. Sleepiness is a thing that can be present in large or small amounts. "There was a lot of sleepiness in her voice" could be used to mean "She sounded very sleepy". "Excessive sleepiness can impair your focus" means being too sleepy can make it difficult to focus. Sleepiness is not a physical object but it is an uncountable noun and can be used as such.
You will find lots of examples were sleepiness is used with an amount which means "shred of" is fine here.
Please see this google book search to see many example of "shred of sleepiness": https://www.google.co.uk/search?tbm=bks&hl=en&q=a+%22shred+of+sleepiness%22