If you are bfing there isn't really anything you need to exclude
If they're dairy or soya intolerant then yes you do.
Both of mine were/are dairy and soya intolerant. I excluded dairy for months. In the early months, it was hard to tell if it made any difference because young babies can be quite windy anyway. But now with my youngest being 10 months, I can have small amounts of dairy (literally a cube of cheese) and DD will get a bit of bum wind but that's it.
I'd stop the probiotics and gripe water. I found gripe water made dd worse. Have you ever drunk too much peppermint tea? It makes you very windy, much like gripe water might.
Dd and ds were very windy for the first 3-4 months. I had to go in a very restrictive diet (basically bland meals, no caffeine, no dairy/soya/spices etc). By 4-5 months they settled down but would have windy episodes if I slipped up. By 6 months I could have small amounts but not worth the hassle.
Once they were on solids, they had to have very plain foods. Both react to tomatoes, citrus, dairy etc (my eldest, ds, grew out of it by 18-24 months). For example, dd had some tomatoes at 8 months and got upset, rubbing her nose etc.
Both of mine also have reflux - goes in hand with intolerances.
You don't really get tests for intolerances as they're not allergies just sensitivities.
Honestly, ditch the gripe and probiotics. Try excluding dairy and soya for two weeks. What kind of solids are you giving baby?