Sounds totally like fluid.
If the fluid is too low then the torque converter cannot fill up and it will be choking on air, a really bad way to transfer power from the engine to the gearbox.
If the fluid is black in color then yeah, change it, and the trans filter.
Usually when transmissions go bad they make a big BANG which can be heard from inside of the car.
But I did have a Ford Auto trans which had a sensor inside it gone and it made it smash into 1st-2nd-3rd.
Seeing as that I was quoted $1,000 for a repair on that one I decided to get a reconditioned one for $650 fitted in shop, I ended up selling the car soon after.
Your options:
#1 Drive it up a hill, stop the car, put your foot on the brake and put the t-bar into neutral or park, then put it back into Drive and take off, if it doesn't want to engage or move forward while going up a hill then you definatley have a fluid level problem.
To top it up, make sure you've driven the car for 10-15 mins, drive it to the auto repair shop and buy the proper fluid for it, then drive it back home and park it on a flat surface, probably the road.
Pop the hood, pull the transmission dipstick out and rub it on the grass to clean it, feed it with two hands back into the transmission and pull it out again to check the fluid, if its on COLD or LOWER then put in about 100mL to 250mL of trans fluid and check the fluid again some other day.
Never EVER check transmission fluid when the car has been sitting for a while, always check it right after doing a short drive. If you check the trans fluid when the engine and trans are still cold then you will ALWAYS get a wrong reading on the dipstick of "cold or hot" or somewhere inbetween.
So if we warm up the engine and transmission, all of that fluid is gonna get sucked up into the parts of the gearbox and is now going to register zero on the same dipstick. a bad thing. It SHOULD be registering at least cold, or hot.
So its a good idea to make sure you check the stick when the transmission is warm, and NEVER when its bone cold.
My best guess is that the fluid level has been checked incorrectly during the last service.
Second option:
#2 Get it checked for free at an auto transmission place.
Third option:
#3 Take off the sump of the transmission and check the fluid for any metal shavings inside of it, replace the gasket and bolt it back up and refill it with sufficient fluid.
If you find metal shavings in the transmission sump then you've got problems.