Will relaxing my hair again hurt it?

Mixed race male black/white with the coarse hair. Back in late November, I relaxed my hair but with relaxer for fine hair normal strength. First time doing it, but I didn't know about hair type. It relaxed it but didn't. Meaning when wet it goes from real tight curls to wavy, however it all tightens back up as it dries. I only relaxed the top of my head because the sides were really short and have been trimmed since. Question is, Will using the relaxer that is for coarse hair be ok on the "pre-relaxed" hair since it's been a while? The relaxer is Africa'a best Coarse/resistant hair, no lye, super strength.