Is it permissible to take injections to induce the expulsion of a blood clot—given that it is unknown whether it is a pregnancy or a menstrual period—bearing in mind that the questioner is medically exhausted and unable to bear a pregnancy?

There is no harm in taking medication that prevents pregnancy. If pregnancy occurs and you are compelled to abort before forty days, there is no harm in that, acting upon the view of the majority of scholars, especially if you are not strong enough for the pregnancy. However, if you are strong enough for it, then patience and not aborting is preferable.