lekarstw jest czesciej uzywane, lekarstw is more populare in Polish, 'Nie mam wiecej lekarstw' means the same, it should be also acceptable
I'm wouldn't be so quick to call "lekarstwa" more popular than "leki" without proper citation, but both are indeed correct.
I'm Polish and I can confirm that word "lekarstwo" is in use and equally popular as "lek".
Added "lekarstw", it's surprising that it wasn't accepted so far. But it has been in other sentences.
I was taught lekarstwo as @pgaj said
I put "juz" at the end this time...(but it didn't work)
For me - native Polish speaker - it would not sound "normal" to say:
"Nie mam leków już". Everyone would say: "Nie mam już leków" (in that order).