Health-wise you're probably better off long term typing the way you already do than learning to type "properly" on a normal horizontally staggered QWERTY board.
There've been some studies, but mostly it's about common sense. It's better to type with your hands in natural positions and involve more muscle groups with smaller combined movements to prevent doing damage or becoming fatigued.
In terms of natural hand position: your wrists should remain straight (in all axes), hands not overly pronated or supinated, forearms low-ish. Most modern desk / keyboard setups force all kinds of weird positions / angles, with upwardly bent wrists being the most common bad position.
If you keep your fingers on the home row, that will tend to force your wrists to bend outwards, too, unless you have 10cm shoulder width.
Split keyboards can help with these (splay and tenting to improve wrist angles).
In terms of movements: if you try to type with only finger movement, you're going to get fatigued quicker than if you involve your whole arm in typing. Smaller movements are better, combining shoulder, arm, hand and finger movements to reach the further keys reduces the chance of fatigue and is healthier than using only finger movements. It helps if the keys are in easy-to-reach, natural positions.
Vertically staggered keys helps with this by positioning the keys in more natural positions, with less overall travel. However, if you're using a board which tends to "lock" your hands in one position for long periods when typing, it's advised to move the board around a little, so you're not keeping your arms and hands in a single position for extended periods. I found I have to do this with my custom ergo split board, since I don't have to move my hands much at all when typing on it.
Another factor in terms of finger joint pain and possibly other keyboard-related health issues is hard bottoming-out. If you're applying force when still when the keys hit bottom, your fingers experience a fair amount of shock, which can be reduced by learning not to keep pressing after the key actuates, as tp says. It doesn't mean not bottoming out, just that you're not adding force any more when the key strikes the bottom.
Then there are character layouts... QWERTY does force a bit more movement than DVORAK or COLEMAK, but it's not as significant in terms of speed, fatigue and hand/wrist health as a split, vertically staggered board would be. I do recommend learning a new character layout at the same time as a new physical layout, though, as you can then keep your old QWERTY muscle memory alive during the transition without affecting your typing speed or accuracy.
