Hello there, this is my first post on here I just joined recently.
I've been trying to Google this issue but because I don't know what is specifically wrong with my car it's hard to pinpoint.
I recently bought this car (November 2021), it is now March 2022. This issue has been getting worse and worse.
I took it to a mechanic and spoke with a handful of my mechanic friends and nobody can pinpoint the issue, I'm going crazy here.
This car is a really good car for a 21-year-old car, and I really do not want to get rid of it. It drives pretty good.

A little bit about the issue:
When the car has been sitting overnight, it starts up great! She drives pretty good and everything.
When I drive the car for 5 minutes (Example: when I go to the gas station down the street) and turn the car off, come out 2 minutes later, my car starts bad.
Sometimes it stalls as it starts???? (I don't even know how that's possible)
The car is not overheating, I always keep an eye out on the gauges and they work fine.
My tank is usually full of gas, I keep it over 3 quarters of a tank.
I fuel up with 87 regular.
There are lights on the dash but they are for Service Vehicle Soon, ABS and Traction (because the previous owner rigged the wires on my front passenger tire when they rubbed against the brakes - mechanic told me this)
There is no check engine light.

All the work I've gotten done to it so far:

• Replaced ignition switch (and everything that goes along with it)
• Got a brand new battery (Optima Yellow Top)
• Got my spark plugs and wires replaced
• Got an oil change at Jiffy Lube
• Filled coolant
• Used Royal Purple Max Clean fuel additive
• Used Heet fuel additive 
• Used Lucas Upper Cylinder Lubricant and Injector Cleaner

Something to note:

• I drove this car from November 1st 2021 - January 2022 not knowing that the car didn't have coolant in it, the previous person had water in there! Once the mechanic put coolant in it, it started driving much better.
• Issue can be replicated 90-95% of the time.
• Issue can be replicated fairly quickly.
• I recently was living in my car in Illinois (in winter time, I had to stay warm) so the car did idle quite a bit.
• A mechanic told me I have a "blocked heater core" I don't know if that could be related to this issue?
• My car does have a small oil leak but a mechanic told me to use 10w30 instead of 5w30 and the car no longer leaks oil.

What I was told it could be:
Starter - but many people say it can't be the starter because it cold starts just fine
Ignition Coils
Fuel pump

I love cars but I do not know the mechanical aspects of a car and I'm a female so I'm afraid of going to a shop and getting ripped off.
Can someone please point me to the right direction? Mr. Kilmer.... At this point you and the Pontiac forum (where I originally posted this thread) are my only hope. Also thank you for making educational videos for people like me!

Here is a YouTube video of my car during cold start then about 30-45 mins later after cold start and a 5 minute drive.

2001 Pontiac Grand Am GT - Doesn't Start Well - What's Wrong With Her????? - YouTube