I was plugging a hole in my tire and maybe i used extra force, but couple of plugs (applied glue that comes with the kit) went into the tire and i could not take them out. On the third try, i was successful. Is there any issue with the plugs inside the tire? Should i go to a mechanic and get them out ?
The will not cause any harm.
Just go drive and find out if you get vibration from the tire balance being off.
It is fine. You put into the tire little bits of rubber. Big deal. They just bounce around in a rubber tire. They can't get out. Not until the tire is changed which could be 10 years later. You went too deep with the plug insertion tool. You stuff it into the tire and then withdraw it and it unhooks from the rubber plug. . This is a short term repair. The proper way to fix it is to remove the tire and apply a patch on the inside of the tire like fixing a bike tire with a patch. except the patch is larger and is glued on the inside of the tire. That will last longer than a plugwhich could start leaking again, so is kind of frowned upon and only meant as a short distance ride, like if they are summer tires, you would take them off to put on winter tires and fix the summer tires with a patch before the next summer came around.