@Jurassicore1996,
If that 3 month job would be applicable to a job you want to pursue, I would include it. If it is not applicable to a job you plan to pursue I would leave it off.
Look at it this way, you are going to have to explain your gap that you have not worked. 3 months one way or another will not change your explanation. You do not have to give details of your medical condition and the exact amount of time you needed off to recover, you simply need to state you had some medical issues that were serious enough, you left your job to get medically sound. You are now completely recovered and would like to pursue a career in xyz.
Most places of employment will not (nor should they) ask personal details. as some things are actually illegal for them to consider in hiring.
Normally I would suggest leaving off a job that was for such a short period, but you said it would help you in pursuing a job you would like so in that case even having 3 months experience would show some skills and show you have an interest in that area of work.