Can I use Flagyl to treat strep throat? I'm allergic to penicillin, bactrum, ceftin (cefuroxime) and levaqon.

No. Flagyl does not treat strep throat, first establish it is indeed strep throat, and see an allergist to go over your drug reactions to determine what you are indeed allergic to and what you can and cannot take. Don't self medicate!
Clindamycin. There are other antibiotics to use, such as clindamycin, for group a streptococcus throat infections. I am concerned about how many antibiotics you are already allergic to. Given your young age it might be worth seeing an infectious diseases specialist and/or allergist to determine what antibiotic options you have before the time you really need them.
Allergic: Everything. I doubt that Flagyl should be on this list. But, Azithromycin may be the option for you.