Tranny/motor?(never seen anything like this)

121,300 miles on it, the truck is  barely broke in..in
my opinion) I don’t bog it in mud, I do take it on
rocky trails with light to medium mud... don’t matte
the pedal in a mud hole, I clean the salt of it from
ice/snow, wash it everytime and clean the
undercarriage and engine bay... I’m 21 YO  I
practically baby it ..I replaced my water pump,
thermostat, and radiator because some store sold
me a faulty part and forgot to clamp the hose on
and lost coolant(also they forgot to add coolant to
the radiator before I left (radiator is fine, no leaks) . I
took it to a store a few days ago because the
temperature gauge was fluctuating to cold, hot,
cold, hot..however I drove it 16 miles then plus 5 to
the shop and it did the same thing fluctuating and
blew a head gasket(I had the same thing happen to
me before with a different car but I drove it 60+
miles and it was a 1990(i think the older motors can
stand heat better than these new ones)....... back to
the Tundra, I had them drain the radiator and do
some kind of tests(bubble, bleed the radiator
whatever you want to call it) after they did that the
hoses on the engine were cold even when running
for 20 minutes(did that test 5 times..same results).
Also, my 2wd switch is activated and it’s in
2wd(power to both back wheels) however it’s
flashing 4WD HI BUT THE SWITCH IS IN 2WD AND
BOTH BACK TIRES ARE SPINNING(might be a
fuse, transfer case). I had this truck for close to
three months.. help, my options are pay 2K to bore
it out and fix it(15 percent chance it’ll work, parts
are $300-500...labor is 22 hrs) or pay 5K for a new
motor..I’m thinking it is something else, please
help.. advice, anything is welcome

It is blowing white smoke