Well, you can check the USCF site out to see if they have received your membership information: http://www.uschess.org/msa. Click on the Look Up a Member link and type in your name on that page. If you are a member then it will give your details there.
I don't recall how long it takes to get your membership card, though I'm sure it isn't as long as three weeks. As to what else you will be getting? Depends on what level of membership you received. You might get the most recent magazine or nothing at all.
For the MCA membership, you probably should either contact the tournament organizer or the MCA directly. If you don't find your information on the USCF website, you should also follow up the tournament organizer to find out how long it might take.
On Dec 17 I won a tournament in which the prize was a USCF membership. On the same day, I purchased a MCA membership. The tournament organizers said that my membership information would be mailed to me. It's been three weeks and nothing has arrived. How long will it take for the info to arrive? And what will I be getting when it does arrive?