My daughter has many of the same problems as yours.
Here are some things that have helped:
1. Make sure your daughter does not eat or drink ANYTHING with sweeteners such as sorbitol, erythritol, mannitol, aspartame, splenda, etc. All of those things, while useful for many people, can cause constipation or other digestive issues in people who take certain meds or who are prone to those issues. Use raw natural local unfiltered honey or organic maple syrup if something needs sweetening. Absolutely no diet sodas, sugar-free gum, etc. Read every label.
2. Eat as many pure recognizable foods as possible. No processed stuff, boxes, mixes, cans, etc. Simple foods in their natural state.
3. Miralax mixed with water or white grape juice, every day.
4. Biofeedback. My daughter went to a women's physical therapy clinic. Usually their clients are new moms or older women who have incontinence (from childbirth, or from diseases or old age), but they also deal with constipation. The therapist inserted a small wire in (it wasn't painful, but a little embarrassing but done very privately and with great sensitivity) and the client learns to recognize the bowel movement feeling, learns to contract certain muscles. My daughter's program included suggestions from the therapist about a bowel movement schedule, proper posture, core strengthening, gentle yoga, and the biofeedback, where my daughter could contract certain muscles and see the computer screen light up when she did it correctly. Her problem is not solely due to meds, she has a connective tissue disease which has impacted her pelvic floor muscle, but the therapist told us at the initial interview that they deal with constipation and incontinence from a wide variety of causes.
5. A low residue eating plan also helped. You can look it up. It basically eliminates rough foods (seeds, nuts, tough meats, high fiber foods), vegetable skins (I peel everything), raw foods (cooked, soft foods are easiest). It's not something you need to stay on forever, but it helps reduce the problem. It gives the colon a break.
6. Lots of water. Not sodas or fruit juice. We buy 2 liter bottles of water so that our daughter can keep track of how much she's had. Filling a bottle or a glass didn't work for her. She tries to drink 2 of the bottles a day.
7. Talk to the pharmacist, not the doctor, about the meds side effects. The pharmacist is the best help in situations like this.
I'm sorry your daughter deals with this. It's so uncomfortable.