Finding the correct medication

Perhaps it isn't a different drug that you need, rather a change in diet. Veggie diets are often quite high in carbohydrates (bread, rice, pasta, cereals, flour, potatoes), which all rather rapidly become sugar in your body, putting up your levels. Many, on this forum, eat Low Carb, High Fat (LCHF) and are able, as a result, to cut down on or give up drugs. As a veggie, you need to concentrate on seeds, nuts, chick peas, lentils, olives, olive oil and vegetables, plus (if acceptable to you) cheese, milk products and eggs. Many here also find that LCHF is good for weight loss. As for constipation, this household has found that simply drinking rather more water helps a lot.
Do tell us more about your diet (if already doing LCHF, my apologies) and what are your blood sugar levels like. I'm afraid I don't have the knowledge to suggest drugs, but someone else will be along soon with more ideas.
Sally

Hi. I agree with the last poster. If you are overweight, then Metformin is the first drug of choice to reduce insulin resistance. Have the Slow Release (SR) version if you suffer stomach problems. Gliclazide is used if, and only if, your pancreatic cells are underperforming. Sitagliptin may also help in that case. If despite weight loss thru low-carbing you still have high blood sugar then ask for the two tests for Late onset T1 (LADA). As you have other auto-immune disease then LADA becomes a bit more likely.

Diabetics control their weight and BG by the amount of carbs they eat and drugs

If you want to lose weight you cut carb. Eat normal amount protein and add healthy oil fat to make up most of the calories that are lost by carb reduction

fatsecret.com/You really need to measure your carb intake for a week there Are lots of hidden carbs
Use a carb counter like fatsecret.com/
Or yourfitnesspal

Personally, I would cut out ALL bread, flour products, pasta, potatoes, cereals, porridge, rice, anything with sugar or honey in it and all fruit and fruit juice for a couple of weeks and see what happens. (Perhaps decrease your carbs over the course of a couple off weeks first to gets used to the idea?) Do you have a blood glucose meter? Ideally you should be testing before and two hours after every meal, at this stage, to see what effect they have. Note, you will still be having some carbs in vegetables, so will not be carb free.
If you are on "ordinary" type 2, sugar levels should come way down on this diet. You can then re-introduce small quantities of favourite things, just one at a single meal, and see if they affect you. If all goes well, you will establish a new healthy-for-you diet.
I would eat cheese, not by the kilo, but modest portions. Fat will not affect your blood sugars and will give you the energy you need.
Some people do say that when they start serious low carb, they feel a bit rough for a few days, but they get through.
This approach worked very well here, but James (who is a very ordinary T2!) doesn't have other health issues.
Sally