Ist es möglich, sich selbst zu schwängern?

The consideration expressed does not work. Especially because, like some in life, it is based on a misunderstanding.

There is no gender change in the sense. A man always remains a man, a woman always a woman. Only in fishes there is the case that male fish convert into female fish because of the other predisposition. But man is bound to his inheritance.
What now happens in truth is a plastic reworking of the body, but without its function. Comparable with glass eyes or the like. This then looks like a corresponding one, but cannot function it.

Accordingly, a change in sex is not possible in the sense and thus the question is actually answered.

However, it is theoretically possible for women to get pregnant by a second egg. This requires artificial fertilization, but it is possible to introduce the cell nucleus of an individual, on which half of chromosomes are located for a human, into a second and thus to fertilize it.

There are two hooks. On the one hand, only women can arise because only men possess the Y chromosome and thus do not occur in an egg cell. Moreover, in this case it would have similar genetic effects as incest with a direct relative. Actually, even worse, because relatives have the possibility that they have individual heir portions which are not carried in themselves, while in self-fertilization only the gene pool of an individual is present and the chance of a shrinking variation is much higher.

Only in a few plant species is self-fertilization or Self-examination is an essential part of the reproduction. These include heirs, which is why it was so suitable as a trial plan for the Mendelian rules.