This can make you sicker faster if the new strain is more aggressive than the strain you already have. If the new strain is resistant to HIV drugs, it may also stop your drugs from working or limit the therapy you take in future.
It is hard to say how common re-infection is, as it has not been seen in large numbers. If you have HIV you will need to find out as much as you can and make your own decision.
You are more likely to re-infect others if you have a detectable viral load, and it is more likely the higher your viral load is.