A UTI is a urinary tract infection, which you'd need antibiotics for or it can progress to a bladder then kidney infection. But since you say it's rare that you can't go pee, then I'd say it's possibly something else. Overall, I'd just go talk to the doctor and mention everything and see what she says. Neither the occasional difficulty passing urine nor the off-and-on bleeding should be happening.
The pee thing is rare not all the time. But the bleeding it'll be like one day I bleed and the next day I won't. Is uti something bad?
Weight gain is common with the shot while on it. Do you have a burning sensation or anything when you try to pee? Is the urge there all the time? Are you sure the blood isn't coming from your urethra and is an actual period (easy test by just wiping each area to see where it's coming from)? If even the first two are true, I'd go to the doctor and get tested for a UTI. Also mention the weight gain if it happened since getting off the shot four months ago and the length of your period.