One term: Mechanical advantage.
You need a pump with the correct mechanical advantage. In the case of an air pump, the size of the piston defines how fast it does its job and how high a pressure you can put into a tire.
Let's say your pump has an effective piston area of 1 square inch (6.5 cm²). That would mean that in order to pump 100 psi (pounds per square inch; 690 kPa = 690 N/m²) you would need to exert 100 pounds of force (or in SI units, 690 kPa * 6.5 cm² = 450 N) onto the pump.
A pump with a smaller piston area will give you an advantage, requiring you to push less hard in order to achieve the same pressure inside the tire, but it also will be slower, as every piston stroke will push in a smaller air volume.
That's why there are some pumps better for low pressure, high volume (like fat MTB tires) and other are better for high pressure, low volume (like skinny road tires).
There are also some pumps with dual mode. They have a mechanism to switch from high volume/low pressure to low volume/high pressure.
The other parameter of a piston is its travel (length of the stroke). A pump with small piston can be "faster" if it has longer stroke, as each stroke will push in more air.
A 700x38c tire is usually wide enough that can be used at lower pressures (I use a set of those and keep them between 40-60 psi (280-410 kPa). Remember most tires have a marking stating the maximum pressure, not necessarily meaning that you must use that pressure. You have to consider your weight, the desired comfort, and the quality of the roads you use.
If you have been setting your tire pressure by hand, and have got good riding performance/ride quality/comfort, and have not had pinch flats (snake bites), then most surely, that pressure is the right one for you on that bike.
If you seriously need to be able to pump your tire higher, consider investing in a pump better suited for higher pressures.
A track pump is the best option to have at home or carry in the car, as it is big and allows you to apply all of your weight to it, they are more comfortable to use and may have an integrated pressure dial. A hand pump is more oriented to be an emergency device to get you out of trouble in case of a flat.
Just in case: Have you calibrated the gauge? If not, compare it with another measuring device. Take several readings to check whether it is giving you the correct reading.