Is there a way that I can read my SD card on my computer (or even cell phone), but it would be locked on any one else's computer (or cell phone)?
Locking SD card is an OS specific feature.
On Nokia s40 (eg: Asha series) and Symbian devices, you can set password for your SD card. On setting the password, other Nokia (ie S40 and Symbian) users will have to enter the password to access it, and even to format it! So once you set a password, you are the supreme owner. But your SD card will become unrecognizable on Androids and PCs.
If you are on Nokia device, open file manager, select SD card -> Option-> set password, or tap and hold SD card -> Set Password.
In android, as far as I know, there is no such built in feature! You may get an app in the store, which is unlikely.