I can't inflate tire. Should I look for another pump?
Most average small/hand pumps are in the 'high volume, low pressure' category. That means they have a big air chamber and are good for inflating a high-volume tire like on a mountain bike with a relatively small number of strokes, but once you reach a certain pressure, often in the realm of not enough for a road bike but maybe around enough for a hybrid, it can become impossible or impractical to go further. Small/portable pumps that work on road bikes do exist. Traditional frame pumps are one example, as are the "mini floor pump" type like the Topeak Road Morphs and its copies. There are also some decent true road mini pumps these days; the Lezyne Road Drive is one that works well. Of note is that many road mini pumps have proven to be basically bad products that don't work very well, and all of them, even the good ones, share the characteristic of needing a high number of strokes and being generally on the tiring side to use.

Most people with road bikes settle on having a floor pump at home, which makes it easy to reach high pressures because your body weight is behind it, and then carrying either one of the above options or a CO2 inflator. If you need a new pump and can only get one, one of the mini floor pump variety is often a good choice, because of the portable pump choices they're the easiest to reach full pressure with, plus they usually have gauges (which most portable pumps don't.)