You might want to look into getting them removed. I had my tonsils removed when I was about 7 years old. One positive to getting your tonsils removed is that it's harder to get strept throat (If you can even get it after your tonsils are removed). Answering your question about side effects to larger tonsils, yes there can be side effects. It's easier to get strept throats. I had inflamed tonsils, and frequently got strept throat. I haven't had strept since my surgery.
It depends on how long it has been since you got over being sick. Sometimes it takes a while for your tonsils to shrink back down to size. Give it some time. If they are still very swollen, then it'd be a good idea to go to your doctors to have it looked at. They will tell you what is the best option for you. good luck