Is a tear near the urethra something to worry about? What can you do to solve this problem?

Natural Healing. The good news is that area has fantastic blood supply and so healing will occur rapidly. Inflammation (red, hot, tender swelling) is the body increasing the blood flow to the injury to bring healing factors to the area and also the veins expand to carry bad stuff away. Dressings and ointments are of no value there. Avoid further trauma to the area and let nature take it's course.
See a urologist. You are obviously concerned, so see a specialuist, urgent care clinic or er.
Nope. A peri-urethral tear should heal well if allowed to. If stitches were needed, your doc would have used dissolvable sutures so don't pull or rub these. Your doc would also make sure your sutures don't distort or pull the urethra to one side. Rinse after voids, don't wipe. This area usually heals very nicely. Take care.