Are you sure you are not feeling pain from medial epicondylitis? Look up "golfers elbow" online and see if the symptoms fit. If this is the case the problem is in the forearm muscles not the bicep. Try this little test hold your hand up like you are an old fashioned traffic cop signaling for a car to stop. Reach over with your other hand to your upheld fingertips. Push hard with your fingertips, the pain should be present. This is a position that should not activate the biceps muscle but should activate the forearm flexors.
There does not necessarily have to be lumps present, they just are if the tear is bad enough. When I had my bout pullups really iritated the area, using a neutral or palms away grip was least painful for me.
Now I'll tell you it doesn't really matter, because the cure if the same rest or scale so you don't make it worse. Ice after exercise (because you probably will) crossfriction massage. Some people like one of those bands, straps that keep pressure on the area . I don't have any experience with those.
I will tell you mine took a long time to heal. I think it was ~12 months if I remember correctly, before I realized hey, I doesn't hurt anymore!