RPMs accelerating without MPH?

For starters, there is no check engine light or any codes that have appeared.
I turned on to the on ramp to get on to the highway. The on-ramp was up hill.
When I turned, the RPMs shot up, meanwhile my speed was barely accelerating. I couldn’t get past 40 MPH for at least a minute. Then it took me another minute to get to 60 MPH.
I tried doing a few small things to see if it was just something simple that was throwing the car off.
First, I immediately went & filled the car up with gas.
Second, I checked the air filter which looked practically brand new.
Third, I checked all fluid levels except for the transmission fluids.
Fourth, I checked it with a code reader to see if anything would appear even though there wasn’t a light on.
It has been doing this for 4 days now with no stop.
Another thing I’ve noticed is there is a soot that is now covering my car. Almost as if it was burning oil out of the exhaust. But it’s not really on the back of the vehicle. It’s mainly on the sides and front.
The engine also sounds louder than it usually does. The sound reminds me of a lawn mower.

I purchased this vehicle about 4 weeks ago for $15K cash straight up.
I did notice (before this problem started) that there was frequently a lag when hitting the gas, but I had assumed it was just how the car is, mainly because I had a Prius before this & it didn’t have to “change gears” so I figured that’s why it felt different to me.
I’m not sure if that has anything to do with the problem & it has just now gotten worse or if they are 2 separate things.