2 years ago I fell from a ladder. Got hip replacement surgery. I still can't run, have pain when carrying heavy things, and feel hip when walking. Normal?

You should not be -- -running for 1 thing. Carrying heavy,what do you mean? Limit yourself to a weight you can handle. Also in my practice I always told patients to me, a replacement should be a little painful, otherwise there is nothing to tell you that you are doing 2 much. When carrying put the weight in the opposite hand. Weak abductors will cause you to lurch to the THA side. Try it and good luck.
Hip replacement. This is not normal. What does your surgeon say? The prosthesis may be loose or mslpisitioned. An X-ray would show the problem. .