Is my 2003 Dodge Neon overheating or not?

Have a 2003 Dodge Neon. Bought it used not too long ago.  Ran GREAT at first. Now
it still runs great out on the highway while it is running. But whether it is a short in town
trip or out of town, when I get to where I'm going and turn it off. I hear a loud bubbling
noise. My son said it was the coolant bubbling up into the reservoir, but it does this
now at the end of every trip, no matter how short the distance is. BUT, the temperature
gauge never shows that it is getting hot. I also see no smoke coming out of the
exhaust and car doesn't run rough. It also vibrates a good bit when it is idling. If I am
stopped at a light, it will vibrate unless I put it in park until it is time to go again. I know
these are two separate problems and the vibration could be motor mounts, but really
need to know about the overheating part. Have an appointment next week that is 50
miles away and don't want to drive it that far if it is overheating. I was told by someone
who was having the same symptoms with her car that it could be a blown head gasket.
Does that sound correct and if it is, is it even worth fixing? I really needed this car for
medical appointments. I am a senior citizen on a fixed income and cannot afford
another one. It ran so great when I got it and I bought it 50 miles away from home and
had no problems getting it home or for several trips thereafter.