Incident with Toyota Aygo

Hello everyone, first of all I am 19 years old and drive with a Toyota Aygo, which is also my own. I have been driving for almost 1 1/2 years now and for a 3/4 year daily by car. Nothing has ever happened so far, but just I drive into the roundabout, blink out to the right, have to stop and suddenly RUMS(!) – I sat like frozen behind my wheel. I drove a smaller VW (I suppose a polo) on the back. I hit the warning blinker directly, I am out of it. We both looked at each other thoroughly and could not detect any damage. It was not even paint off, the license plate was not bent, let alone a bump to see. Since we both were in a hurry and both wanted to get out of this situation as quickly as possible, we agreed to let the event stand like this. For me, this was ok in this situation, because we both wanted to leave this situation as soon as possible. e said there was no damage and we both went well! But somehow now I feel that it might have been a mistake to continue driving without changing numbers. So I quickly looked for a forum to get some reliable and quick advice. One question would be, for example, which non-visible damage could have occurred (e.g. a friend said that my exhaust was definitely moved now. even if what consequences were there? has that?) and now I absolutely have to drive to the workshop? Of course I would have to pay for all the costs.. I would like to thank you very much for your help!