I have been on birth control for 4 mnthsi had intercourse 6 days later I having lightbrown/red spottingthenheavierwithcrampingnauseaheartburnpregnant?

Possible. You could be pregnant. Most likely that is not the case. It could be spotting related to the birth control pills. Taking a pregnancy test is worthwhile.
No likely. Assuming one takes the birth control pill regularly without missing any pills, and has been on the same pill for at least one month, it is unlikely (but not impossible) to be pregnant after intercourse. However, see your doctor if you are still concerned, or do a home pregnancy test.