Sounds very much like a hemorrhoid issue. Yes, working out can cause a hemorrhoid especially if you are lifting weights or doing any type of leg or abdomen work where you strain.
Hemorrhoids don't have to cause pain, no. Especially if they are internal and/or small. The external hemorrhoids can cause more pain and itching than the internal ones but both can be bothersome. If you have an internal hemorrhoid and it continues to get bigger (over time), yours will start to bother you at times as well.