Is there really anything that can eliminate a pimple overnight?

The answer is maybe, but not usually.

The absolute best advice I can give you is to not touch, rub, pick or sqeeze! The only exception to this rule, is taking two Q-tips to squeeze any visible superficial white puss. When you manipulate a pimple in any way, and especially if you squeeze it more deeply trying to get to its base, you set off a series of reactions that lead to even more inflammation and a larger more visible lesion. Every time. There are no exceptions!

The key is not causing more inflammation and reducing the existing inflammation at the same time. Over drying the acne spot will also cause it to get worse.

Options to dry up the pimple as quickly as possible are:

Very precicely, apply a toothepick to the spot (not the surrounding area) with a small drop of argan, vitamin E, or olive oil followed by toothpaste. This has to be very precise or you will end up with a bright red, irritated area wherever the toothepaste touched your skin.
Applying ice is also helpful but not convenient to do all day. If you have any Duac, Tazorac, or another prescription topical, apply a dollop in the same way above. Always apply some oil first to reduce inflammation and prevent the skin from drying out. You will have to sleep on your back so you don't disturb the treatment.
You can see a dermatologist for a shot of steroids, but, this has three disadvantages. One, it doesn't always work and i can take two to three days to notice improvement. Two, it can lead to a little divot in the skin that can take up to six months to fill back in. Three, it can prolong healing in the long run. You sacrifice getting rid of the swelling and size for a persistent smaller acne lesion that takes a while to heal. This is because steroids delay healing.
We cannot emphasize this enough...NOT TOUCHING the acne spot is the absolute best, most effective treatment.

And if the acne spot has reached the point of infection, a little zap of your aesthetician's germicidal wand can be very helpful.