Poor accelleration and vibration

Yes sounds like a misfire. Make and the year it was made?

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Year, make and model? Engine or transmission jerking? Vibrations?

sounds like you have a manual transmission. ?
Worn Clutch plates will give these symptoms
The clutch plates rub together and provide connection between the gear box and the drive shaft if not worn.
Also check the cable for the clutch is not loose and needs a surclip to hold it in at the firewall.
Check if Hydraulic Clutch that there is adequate clutch fluid if low might have leaking clutch master cyclinder

I have experienced this in a car I owned.
Not a lot of fun . Resulted in needing a Tow to repair garage and new clutch was AUD $1200 a couple of years ago.

Fuel filter first thing to check after having contaminated fuel removed. Clogged fuel injectors, crank or cam sensors.

Flashing check engine light is a SERIOUS misfire. Read this post
Flashing check engine light is serious Ricks Free Auto Repair Advice

give it a visual check and if all the wires look good you should replace the sensor, consult a chilton manual for specifics

You could have picked up some bad gas, but it's more likely that your gas cap is not sealed all the way - a common problem. Tighten the cap - if it's the problem the car will start running smoothly almost immediately and the check engine light will reset itself in a day or two.

It sounds like its a coilpack. Its hard to say whick one, but it can have hot fire running slow. Then when the demand go's up and running faster it fails. So it might be a little expensive but I would go ahead and replace all of em. Prob lesss than 100 tho.

87 octane ,,,you kidding ---more like 95 octane .But this has nothing to do with the vibration and check engine light,forget having the codes read get the dealer to look at it

Hi, i recommend changing the fuel filter and pump as well. this is common when you have restricted fuel flow through the fuel lines due to a clogged filter and faulty pump. I would also recommend having the injectors purged with a fuel additive called Techtron injector/tank treatment. this will clean out the carbon build up in the intake and it will also clean the injectors as well.

EXTRA--

I recommend applying a tune up by adding new wires and plugs. this is extra maintenance and it is optional. i do recommend applying this along with the above suggestions.

Please rate and have a great day:)