A single word for "stuck between a rock and a hard place"

It's two words (and it's a noun), but one possible term is "Sophie's choice."

Between Scylla and Charybdis is an older form of the same expression. This refers to the straits of Messina between mainland Italy and Sicily, and the term dire straits (although admittedly two words) still sums up the situation quite well.

Using a single word, you may say "I was squeezed".

"To squeeze" means to exert pressure to force someone into a difficult situation.

Example: Small ​businesses are being squeezed by ​heavy ​taxation.

When playing bridge, a squeeze is a strategy that forces the opponent to "choose" what part of his defense he will renounce.

I'll suggest 'pestled', the verbal adjective (or whichever form of the verb you might have a use for) from 'pestle':

1. trans. To beat, pound, or grind with or as with a pestle. Also in extended use.
   ...
2. intr. To use or work with a pestle.

["pestle, v.". OED Online. September 2015. Oxford University Press. http://www.oed.com/view/Entry/141773?rskey=e0VuKk&result=5&isAdvanced=false (accessed November 04, 2015).]

Your use, as you example it, would be an "extended use", and perhaps so far extended as to be figurative:

This left me pestled.

Use of this word would suggest the rock and hard place imagery without spelling it out.

Not a single word but a pretty explicit idiom...

a no-win situation

A no-win situation, also called a lose-lose situation, is one where a person has choices, but no choice leads to a net gain. For example, if an executioner offers the condemned the choice of dying by being hanged, shot, or poisoned, since all choices lead to death, the condemned is in a no-win situation. This bleak situation gives the chooser little room: whatever choice is made, the person making it will lose their life. Less drastic situations might also be considered no-win situations: if one has a choice for lunch between a ham sandwich and a roast beef sandwich, but is a vegetarian or has a wheat allergy, that might be considered a no-win situation. Wikipeida

How about "stymied"?

stymied is a past tense form of stymie: to ​prevent something from ​happening or someone from ​achieving a ​purpose

It's missing the element of there being precisely two equally bad alternatives, but at least it is a single word adjective that describes the situation.

This left me between a rock and a hard place.

This left me in a dilema.

This left me stymied.

Another possibility is "conflicted".

to be confused about what choice to make, especially when the decision involves strong beliefs or opinions

Depending on the situation, these might work:

This left me between a rock and a hard place.

This left me in a dilemma.

This left me conflicted.

"Horns of a dilemma, faced with two equally undesirable alternatives. In Greek logic a lemma was a premise, a matter taken for granted in an argument, whereas a dilemma (a double lemma) was an either/or proposition. The Romans called this an argumentum cornutum, or “horned argument,” because one could be caught on either horn."