You should talk to your DM about this. The rules are confusing and vague, because D&D is not usually a game where type of musical instrument matters. I don't think the designers spent much time on them. That's okay — but it generally means this isn't part of the rules-as-written which stand up to much hard thinking.
In most cases where there is cause to think about it, the DM should adjudicate either something much more relaxed than a a strict reading of the table might imply, or (in rare cases) substitute a more considered system.
In my games, I let bards be proficient in any instrument they want to be with no limits. This is because in all my years running and playing D&D, it's never mattered at all. It is entirely a bit of flavor, and if a bard can't have "I wow the locals at the tavern with whatever musical instrument is at hand" as flavor, what's the point of even being a bard? I think this is entirely appropriate in almost all games.
In fact, if a player wanted to be specially good at a particular instrument, I'd be inclined to let them have double proficiency with that one. Again, this is because I can count the number of times it would really matter in all the games I've ever played in a case other than the bard showing off their character on... zero fingers. This is right there in the same vein as "can my paladin's armor have a fancy helm which looks really cool?" or "my ranger's cat has spots".
Although it's just one "pillar" of the game, most of the mechanics of D&D focus on combat (5E, but to a large degree other editions as well). Most of the rest are to do with movement, exploration, and logistics. There's just not much in the game rules-as-written for instrument proficiency to interact with — let alone really worrying about instrument types.
There's no different die sizes, no way they might affect audiences differently, no rules about being easier to use in the middle of a battle. Nothing at all except the different prices, which are, not surprisingly, weird and arbitrary and low-design-effort. (Double-reed wind instrument? 2 gp. A stick cut into a whistle? Also 2 gp. Complicated horn with valves? Bump that up to 3 gp. Piece of goat skin stretched over a frame? 6 gp! A box with four strings on it? 25 gp, of course.) So, it really doesn't matter to the game which instrument proficiencies you have, and in most cases it's just a strange hobbling.
Of course, some games may go the other way. Musical instruments and skill with different types could be an important feature of the setting or plot. In this case, the rules need the opposite fix: house rules to provide satisfying differentiation.