You use though to introduce a statement in a subordinate clause which contrasts with the statement in the main clause. You often use though to introduce a fact which you regard as less important than the fact in the main clause.
You use though to introduce a subordinate clause which gives some information that is relevant to the main clause and weakens the force of what it is saying.
You can say though I say so myself or even though I say it myself when you are praising yourself or something you have done, but do not want to sound too proud.