When I drive my car, is fine for the first twenty minutes. After which time, the car drives like the E brake is on. Further, when I’m in city streets, the rpms go really high just to hit 25 mph. When I take my foot off the gas, the car gradually slows to the point where the car stops while in drive. Even if i press the gas, I have to press hard before the car moves. And when it does move, is like the E brake is on because it acts like it doesn’t want to move. While traveling, is hard to reach 40 mph without the engine feeling heavily over worked.
Sounds like the brake calipers are binding.
I’ve seen this before. They get warm and apply the brakes.
next time it happens get out and feel the rims. A rim hotter than the others has a dragging brake.
It’s a good practice to flush out the old brake fluid every 2-3 years, which extends the life of brake components.
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CAREFULLY touch the wheels. If it is sticking that bad, it could be really hot. Be careful. 
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I will use maximum restraint and not ask if it is the Fiat 500 that ends up with a blue pill in it’s fuel tank from a certain commercial.
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What year is the car and how many miles does it have on it?
Engine option if appropriate?
Transmission (manual/automatic/CVT)?
As others have suggested, this could well be a problem with a dragging brake caliper or two.
Or, it could be a transmission-related problem.
If this Hyundai Elantra–of undisclosed odometer mileage and undisclosed transmission type–has an automatic transmission, that leads to the following questions:
Have you checked the level, color, and odor of the transmission fluid?
When–if ever–was the transmission fluid changed?
It’s a 2003 Hyundai Elantra automatic transmission with 158k miles.
I topped off the transmission fluid a few days ago. Apparently it was completely empty. I out four quarts but I didn’t change the filter or gasket (if there is one).
Starting to sound more like a transmission problem than a brake problem. Your next step is probably a proper transmission service, meaning drop the pan, change the filter, and replace w/fresh. Note that what a “proper service” means depends on the manufacturer of the vehicle, so verify by consulting the owner’s manual or ask a dealership if you aren’t sure.
It sounds like the damage is done, a transmission will be damaged rather quickly by driving without fluid with the engine racing.
Yup!
If the OP’s engine was “racing”, and the trans needed 4 qts in order to bring it up to the full mark, I would be very surprised if this transmission has more than a few days of life left in it.
I would advise the OP to begin formulating his strategy (repair of transmission or replacement of car) immediately before he winds up stranded on the side of the road.
If he opts for overhauling of the transmission, be sure to avoid chain-run places like Lee Myles, Cottman, Mr. Transmission or–God forbid–AAMCO.
Look for an independently-run trans shop that has been in business for at least 3 years, and you will get better workmanship, and perhaps even a lower price, as compared to those chain-run shops.
Interesting enough, I’ve out my hand near the tire and I can definitely feel more heat coming from the left tire than the entire or any other part of the car. In fact, that left tire has smoke coming from it which forces me to park it and let it cool off before continuing otherwise the car pretty much drags until it’s cool again.
Then you have a binding caliper…or maybe two. But with the age of the vehicle…it may only be the flexible brake lines that are keeping the brakes from releasing.
You should have it towed to a proper mechanic and have them replace the bad caliper or lines and new brakes.
Also have them drain the transmission and change the fluid.
If the calipers were the problem you may have the transmission over filled. At least you will get it serviced.
Yosemite
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