The key feeling that you have expressed is loneliness, something that all of us who began by ourselves have experienced.
Start looking for a partner NOW. Do not put off doing so. When you discuss partnership with someone, be very straightforward about your expectations, your experience, and your financial situation.
Ladydance is correct that practice is very important. While practicing by yourself is necessary, so is working with another amateur.
A couple of tips may help. First, don't depend on the dance-partner websites, especially the ones that charge a fee. Second, don't expect your studio to help you find one; chances are that they don't want you to have a partner and will try to convince you that you're better off without one. Also, don't let them tell you that you're not ready for one yet.
I need to make it clear that I mean a DANCE partner and not an object of romance. If a personal relationship happens, fine, but the lack of a gleam in the eyes shouldn't keep two students from dancing together.
It is very important that you do NOT let yourself "become enamored" of your instructor, a nearly universal pitfall for beginners. This person's primary obligation is to make money for the studio. Don't ever forget that fact.
I have to second Belle's concern about your instructor, who doesn't sound the least bit professional. It also bothers me that the more experienced students have not been more encouraging and supportive.
You've signed a contract so go ahead and complete it while you look for a partner (I bought out of my first contract). Just remember, as terence likes to point out, ballroom dance instruction is a business and you are the customer. You may not always be right but you're never wrong and there are other studios.
Best wishes and remember that we're always here to help.
jj