Alternative for overchallenged

You can use the word overtaxed.

Overtaxed verb 2 Make excessive demands on (a person’s strength, abilities, etc.): do athletes overtax their hearts? - ODO

Consider swamped, already mentioned in @Andy_Fielding answer.

Definition: to be plunged into or overwhelmed with something, especially something that keeps one busy, worried, etc.

Example: I’m sorry I didn’t respond to your email. I’m really swamped with work right now.

Also overstrectched.

"overstrecht" definition : to make excessive demands or put excessive pressure on (oneself, finances, etc); overburden.

Burdened — TFD

to load or overload;
"she walked forwards burdened with a wooden box"

cause (someone) worry, hardship, or distress.
"they were not yet burdened with adult responsibility"

_{Other suggestions: encumbered, overloaded, hampered, weigh down}

Those suggestions are good when you're referring to a single task.

When you're referring to multiple tasks, a good word is swamped:

"I can't handle more work this week—I'm already swamped!"

It creates an image of sinking into a swamp, being overwhelmed by water (and maybe crocodiles!).

Consider deluged.

Definition: a large amount of things that come at the same time

Example: he has been deluged with offers of work.