Send SAT or ACT scores? Or both?

I scored a 30 on my ACT (33 English/ 26 Math/ 35 Reading/ 26 Science) and a 1340 on my SAT (710 English/ 630 Math). The only thing stopping me from sending only my ACT score is the fact that I scored 7/12 on my ACT writing and 22/24 on my SAT writing. This concerns me because I am applying to a few pretty competitive schools. Would sending both even make a difference? My intended major is public health if that makes any difference.

Any input is appreciated!