Is it a Honda or is it an Elantra? It can't be both.

What do you mean by "feels like a push"?

Have you scanned it for codes or looked at live data?

2015 Honda elantra

No such car exists, I'm assuming you meant a HYUNDAI Elantra.

Please provide the millage? trim level? transmission type? was the firmware ever undated? was transmission ever serviced?

If it's an Elantra GT, the diagnosis would be completely different.

I'll assume it's not a GT, but a 6 speed automatic Elantra sedan.

By the sounds of things your transmission is pushing and jerking,

to verify it is the automatic axle causing the jerking, try shifting gears manual in M mode (if equipped)

In such cases, as the Owner's manual "OWNER MAINTENANCE" section (detailing things you, the owner, must perform when operating an Elantra, in addition to scheduled maintenance!) states "If any (...) changes in the operation of your transaxle occurs, check the transaxle fluid level" in Perform that procedure as it is shown in the maintenance section of the manual.

Please post what color is the fluid? does it smell? any chunks in the fluid? does the fluid look metallic?

Additionally note that under the "MAINTENANCE UNDER SEVERE USAGE CONDITIONS" section you are instructed to replace automatic transmission fluid every 60,000 miles if the car was operated under any of the following conditionsL: "Repeatedly driving short distance", "Driving on uphill, downhill, or mountain road", "Driving on rough (...) roads", "Driving in sandy areas", "Driving in heavy traffic area over 90°F""

Was the car operated under such conditions? and was the transmission fluid replaced?

Please post the findings and use the mentions feature (for example, @Dan) to notify forum members that the thread was updated.