Help me please.

Hi,
Sorry to hear. I’m going to give you some info, so you understand. Not trying to intimidate you. Only help. First, I’d recommend, for now, you square away the Transmission issue prior to worrying about “flooring it”.lol.
The Transmission has 2 lines from it that enter/exit the radiator to keep the Trans oil cool, some run a stand-an Oil cooler, or just run as-is, stock to the side of the radiator..Either way, the lines are mostly steel & they/the Radiator may sometimes get clogged where it exits & returns to the Transmission. Check for leaks.
There’s 2 schools of thought, here
Changing the tranny fluid and replacing the filter should be done every 12K, is the most logical choice to bring it to AAmco or a similar shop, so you know it’s done right. If you want to mention it’s shifting issue, they may take a different approach. Unlike a dealer, more constructive info than costly. Sam I will take it for a quick drive free, then make a plan. A Dealer will want huge amounts of $$.
So, I’d not bring it to a Dealer, nor to a shop like Jiffy lube. If the fluid hasn’t been changed in 12-12K Miles, or 30K miles.
Parts will cost ablout 40$ or more in Trans fluid, about 60& in materials, about 100-120$,for the job done ri just FYI.
If it hasn’t been done in a long time they’ll need to drain & maybe flush the Tranny, empty the Converter & refill. LOTS of oil! Get it yourself, cheaper. A decent Scantool would allow you to read the tranny’s pump pressure, and more. Manual will tell you why.
Torque Converter, too, Flushing the system as well, it’s easily done if you have the right. tools. Again, you can still do this. Maybe do it next time, when you’re more sure of it. I don’t think your Tranny’s bad, likely lacking maintenance.and/or fluid.
Aamco will tell you what’s best is all, Will bthe engine issue, may be related. Bring it in, ask for opinions.
Some won’t drain all the fluid as the media circulating around is actually helping certain Transmission function, IF it’s high mileage, non maintained, not beaten hard, should be fine.
I’ll work with you on the engine, this should be addressed first, K
.
Before you make a decision...
First, Check the level of the fluid on the dipstick, and take a whiff of it, it shouldn’t smell burnt and should be a light reddish color, and to the indicated level on the stick, (read the stick, engine off, follow instructions, replace). “Car running in park, engine warm, reinstalle on”, etc
Many overlook the fact changing the automatic transmission & filter is a required process, and not doing it can lead to very bad outcomes. As important as your motor.
First off:
Do the basics, check the transmission fluid, has it ever been changed, if it’s low, add the correct type, per instructed.
Does it “slam” into gear when the 1st to second issue engagement finally occurs, act the same, car hot or cold?
If fluid’s low, isn’t black or brown, top it off as instructed. Follow the tranny lines, make sure they’re not kinked, restricting flow.
How many miles on the Car? Has the maintenance been kept up on engine oil (3-5K) and Transmission oil (12k-15K).?
Is there a Tune (CPU reflash) that the Vehicle is running at this point, or is it bone stock? Any bolt-on’s parts you’ve added, and how did this start occurring, suddenly..or start & get worse over time?
Is there any Codes (CEL’s) popping up, if not, plug in a Scantool and check anyways, sometimes they do not pop up. If you don’t have one, you can take it to Advanced Auto & they will do it for you.
A Scantool & a Haynes Shop Manual is something worth buying, they’re necessary & inexpensive, with a 96+ Mustang (OBD-2)
This can save you lots of time & money. If a code pops up, it’s a clue to an issue. Not the issue 9x out of 10.. So, If you like the car, read that shop manual cover to cover. You’ll learn a lot, & always have it for reference.
Please answer the few questions asked, service history, mileage, pull the dipstick, odor, was fluid low? Etc, I’ll help you make more informed decision
Good luck, post results, please.
Good luck!
-John