Why does a clinical thermometer have a constriction and a laboratary thermometer does not?

The main reason is to make it stay at the maximum point so you get an accurate reading. Without the constriction the mercury would drop as soon as it was taken out and couldn't show the temperature where it was just taken.
(Source was my school physics book)

Laboratory thermometers need to be sensitive to changes in temperature - when you put one in a cooler environment (such as a beaker of ice water), you want it to drop down to that temperature without having to shake it while you measure. It is read while immersed in the substance whose temperature is being measured, so it does not have to be held at it's highest temperature in the same way a clinical thermometer does.

There is a special type of thermometer called a high-low thermometer (in the general science classroom when setting up a small weather station) which DOES have constrictions it the two side-by side thermometers used, so that it shows the highest and lowest temperatures recorded over the reading period, not the current temperature.

source - years of teaching science

As satguru points out, the mercury drops as soon as the thermometer is taken out of the orifice (whichever one!). Temperatures of patients could be taken in situ, but this would entail bending down close to a probably already upset patient, and getting rather close to the orifice concerned. Not a good idea.... Scientific thermometers are read in situ for simple lab processes, and rather more complex equipment is used where this is not practicable for safety reasons. Similar remote sensing would not be feasible for patient care - cost and size being two reasons.

As to 'high-low', to me they're 'max-min' and the ones I've come across don't have two thermometers, but instead one U shaped one with little steel pointers in each leg. One side pushes the pointer up when temp goes up, the other does the same when the temp goes down. (Zeroing is done with a small magnet.)
http://www.weatherforschools.me.uk/html/maxmin.html

I can't see how the two side by side work - both will go up when temp rises, and stay there if there's a constriction. Are you sure that's not the wet-dry instrument, where one has a wick keeping the bulb wet that you're thinking of?