I would just get some bra pads and bear with it for three months. Change them often so you don't get a yeast infection. Trying to get the colostrum to dry up before delivery may not be healthy.
I have heard of people using the breast shells to collect leaking milk, and then storing it to give to your baby. I don't have any experience with this, but I think they are like a nipple protector, and stay inside your bra.
If you do get engorged after your baby is born, lean over a sink or bowl full of lukewarm water. The milk will run out and relieve some of the pressure, but will not empty enough to increase your supply. Avoid hot showers and hot compresses, they will feel good but release too much milk. Cold compresses are okay, or soothies inside the bra feel good.
Even though you don't plan on breastfeeding, still avoid underwire bras or too tight bras until after the milk has dried up so you won't get a plugged duct or mastitis.
Have you considered taking a DHA/Omega-3 supplement while pregnant? That can help both you and your baby.
Also, are you getting good prenatal care? Be on the watch for signs of preterm labor. I don't know if leaking milk early is a sign of earlier labor, but my first was early and I had leaking early. Just know the signs and be on the watch.
I'm not trying to second guess you, but have you checked with the pediatrician about the meds you are on? They may give you a different answer than another doctor, as the well-being of infants is your specialty.
Happy and healthy pregnancy and birth to you!