Difficulty inflating my bike tire
It sounds like your pump is not on the valve properly, so instead of inflating the tire you're just pressurizing the inside of your pump.

Does your bike have Schrader valves (the kind you see on a car) or Presta valves (skinnier, with a kind of pointy top)?

If it has Presta valves, make sure the top of the valve is unscrewed.  There's a little nut that you can thread up, and you need to do that before you can put air in to the tire.

Also, try wiggling the pump nozzle around on the valve while you push down on the pump handle, you should be able to hear the change as air starts going in to the tire.

Image of a closed Presta valve:



Image of an open Presta valve:



Image of a Schrader valve: