There's a lot that could cause problems with your transmission that can be addressed short of a full rebuild. First, how many miles do you have on the car? Have you been good about changing transmission fluid, or have you fallen for the "lifetime fluid" B.S.? (No disrespect intended, by the way.) If the mileage is low and/or you've been good about changing the fluid every 40K miles or so, it's likely that the internals of the transmission are fine, especially if you've also treated the transmission nicely, e.g., no loaded torque converter burnouts, etc.
If I were you, I'd do a fluid flush including the torque converter (assuming it hasn't been done in at least 25K miles). I'd also check vacuum hoses for leaks. Check the vacuum modulator. Check linkages, and if you have a kick-down switch, check that. Sometimes they get stuck and the transmissions then don't upshift until the engine hits redline.
As for your fluid coming out of the dipstick tube, that's very weird. Was it much? Did it look foamy? If you have coolant entering the transmission from a faulty radiator, it would make the fluid look like a strawberry shake, e.g., kind of milky pink. If that's the case, stop driving the car immediately, replace the radiator, and then do several flushes of transmission fluid and pray to the automotive gods that your transmission somehow survives.
By the way, if you haven't, watch some of Kent Bergsma's YouTube videos on the topic. This link is to part 2 of a video where he's stumped by a transmission problem.
<i>Where our own '99 C280 developed a weird transmission problem after sitting for 2 months, which then vanished just as mysteriously.</i>