Let's just start by saying that transpiring/sweating is a completely normal process. It is your body's way to stay cool when it gets warm. Almost all of us use deodorant at least once a day. Although they are great to reduce our BO there is some disadvantage to regular deodorant that might make you reconsider a more sustainable option.
Disadvantages of regular deodorant
Personal care products like deodorant, often contain aluminum, parabens, and properly glycol. Research has shown that aluminum can enter our body and affect our hormone system (even in only every tiny amount) so, I prefer to avoid this as much as I can.
Deodorant is also often alcohol/ethanol-based which may cause your skin to become dry, tight, and itchy.
Unlike the stick deodorant, the spray deodorant contains aerosols. Luckily, chlorofluorocarbons are no longer present in these types of deodorants. These were known to affect the ozone layer. However, butane and isobutene are still present and cause irritation to your skin (and eyes and lungs if not aimed accurately).
Waste production is another important reason to switch to a more sustainable alternative. Every 2-3 months a can/bottle of deodorant is used and ends up in landfills. Over a lifetime, this is a huge amount that could have been avoided if a more sustainable option was chosen.
Go au natural
Going au natural without any form of deodorant can be liberating but it is not for everyone. As I work out on an almost daily basis, this was not really on an option for me but I greatly admire people who do. Besides, it can also save you a lot of money.
I read that there might be a transition period of a few weeks where your armpits need to adjust to the new routine. This may cause you to transpire more during this time but afterward, this should normalize again.
Using a natural deodorant is my go-to option. I choose a brand that is free from aluminum (for the above reason) and backing soda. Backing soda is very alkaline (with a pH of 9) while your skin is rather acidic (with a pH of about 5). To keep your skin healthy you don't want to affect the pH balance and damage your skin so try to avoid baking soda on your skin if you can.
I use a deodorant bar from Ethique as this is completely waste-free. I have been using it for over 6 months now and I have not even used half of it. So it lasts a lot longer than expected. The bar is slightly scented but I don't smell that on me once I use it. It doesn't prevent me from sweating but it does keep the BO at bay after a hot day or a workout which is basically all I ask for in a deodorant.
There are more brands out there that are completely natural. There are even ones that you can push up from the bottom so you could use it in a similar way to the regular deodorant if that is something you prefer.
I love DIYing my own cosmetics and there are great recipes out there but I suggest first trying something store-bought to see if you actually like using natural deodorant. It would be a waste if you purchase all the ingredients to make one yourself and then finding you don't like what you have made.
I hope you find this information useful and will help you transition to a more sustainable alternative to your deodorant.