Has the cash been deducted from your credit card? I suspect that the answer to this is no.

I would say that this has disappeared into the infamous "awaiting ticketing" black hole.

UA is usually e-ticket unless you happen to be travelling with an infant, and something that they can do in less than 10 minutes if they so chose.

You need to follow up, tell them that you need ticket numbers for a visa application otherwise this could get nasty and you could end up losing the booking altogether. Check your booking on checkmytrip.com and e-ticket numbers should appear when it has been ticketed.

Hope that helps