Saline (sodium chloride) injections used as placebos in clinical trials tend to be very innocuous. They can sometimes cause a little temporary soreness at the site of the injection due to the small tear in skin and muscle created by the needle, but they do little beyond that. The soreness and heaviness that is more often associated with flu shots and other vaccines are seldom reported.
Most likely, you will only feel the prick of the initial injection and nothing more. For this reason, saline shots tend to be ineffective placebos, as participants could infer from the lack of symptoms and side effects that they did not receive the actual medicine. To account for this, many clinical trials use alternatives to saline placebos, such as the meningitis vaccine, for the control group. These active placebos are much more likely to cause noticeable side effects, thus better maintaining the integrity of the trial.
This is not to say that there are never side effects associated with saline injections. Under rare circumstances, these injections can cause swelling at the site of the injection, redness, soreness, and even fever. However, this is more often the result of an unintended infection resulting from a non-sterile needle or a pathogen entering the site of the injection, not the result of the saline itself.