Unless there is a typo in your question, I think that problem is that your untrained voice has a very small range, i.e. less than an octave (or at least, that you think it only has a small range). A good range for a trained contralto voice (often called just "alto" in a female choir) would be F3 or G3 up to about E5, not E4. A "second alto" (singing the lowest part in a 4-part female choir) would probably be OK with an upper range of C5 not E5.
To avoid any confusion, using the (American) standard terminology, F3 is a fifth below middle C, and C5 an octave above middle C, and E5 a third above C5.
A "professional standard" contralto would have a more extended top range - I know one who can hit a Bb5, which is higher than some sopranos who sing in choirs can manage.
There is no problem with the low end of your range. Some contraltos can comfortably sing male tenor parts that go down to C3 (an octave below middle C) but F3 won't be a problem.
Talk to the choir director or conductor. If they can't give you some one-to-one basic voice training lessons themselves (not necessarily for free, of course) they will certainly know somebody who can.
Problems with vocal range are often more "in the mind" than physical limitations. A few lessons with a good teacher may be all you need to get you singing in the choir.