The numbers.....

30,000 orchid species

100,000 registered hybrids

To clarify, you purchased the plant in Mexico?

If you saw the plant in bloom or a photo of similar you could look through google to narrow it down to a type "Cattleya", "Oncidium" and so on

"TJ" would be Trader Joe's in this instance. The ones in my area get culls (undersized specimens) from a huge operation in California. As pointed out above there are too many kinds to be able to tell what yours is using only the view you have posted here. And the flowers need to be seen to have any real idea.

Orchids from Trader Joe's are inexpensive enough to be treated like longlasting cut flowers.........enjoy them in bloom for as long as they provide it and then toss 'em!! Yes, some species do rebloom relatively easily when grown indoors but others require more manipulation than the average non-orchidist is prepared to provide.......or knows how to!

Where else can one find flowers that last for 2-3 months (or longer) for less than $20??

were you thinking Tijuana??? ... that was the only tj my midwest brain came up with ... lol ...

The leaves are sort of like a miniature cattleya hybrid (or Sophronitis, Laelia, Brassavola, etc). But I'd have to see a better view of pseudobulbs and rhizomes (if there are some) to know for sure whether it's a cattleya-type hybrid. A photo of the bloom would go a long ways to narrowing down the playing field.

http://myorchidcare.com/orchid-care/Orchid-Identification.html

To me it looks like multiple phals potted together, hard to tell from the photo. Whatever it is, it looks to be dehydrated. That would mean that it's not being watered enough, or there is root damage.