roof nails sticking up

I have budgeted myself to have a new roof installed within two years.
There is an small area of water damage in my bedroom that looked like
was attempted to be repaired by the previous owner, and had new water
damage once in two years.. I have noticed that there are nails starting
to stick up under the shingles, and have even started to pop out above
the shingles in a few places. I am having my garage roof replaced next
week. I had several roofers out for estimates, and had them look at the
house's roof with these problems. They said that the house's roof does
not necessarily have to be replaced right away..

Should I tap back the nails and caulk them until I get the roof
replaced? Is that even necessary to do, and I can just ride out until
later on when I get the new roof put on?

If the nails are popping up it's because they are not being held by the
sheathing. Often because it is soft or rotten. At minimum as a band-aid,
put some roofing cement on the popped up nail where it enters the roof.
This will insure the hole is sealed when the nail is banged back in. Bang
the nail back in if the sheathing will hold it. Cover the nail head with
roofing cement.

On the ones that have even started to pop out above the shingles in a few
places, replace the shingle if possible. If not then do the above with
the nail. Put lots of cement on the nail head so when you press the
shingled back down the cement will seal the pop-thru hole.

Not a roofer. Just my unprofessional .02.

If the nails that are backing out are framing nails, I pull the nails
(with a wood protector block under the hammer). I next check with a
piece of stiff wire to see if the nail was into something below the
sheathing. If not, use roof cement or silicone to seal hole. If
framing is felt under hole, use deck screw slightly larger and about
1/2 longer than nail to refasten in same hole, then seal hole in
shingles.