Depends.

1) H4 can still go to school, no need to transfer to F1 unless you are offered assistantship. Then you'd better get help from your ISO to do status transfer.
2) H4 might be able to pay in-state tuition depending on the policy of your school.
3) Getting F1 visa from Canada/Mexico may not be a good idea. Your chances are slim unless you already got the transfer approval from USCIS and have good reasons for getting F1 visa. Otherwise, go back to China to get F1 visa probably is the fastest but you need to take the risks, too.