For the vast majority of men, the latex material used in condoms and the materials they use (such as spermicide) do not do damage to the skin on your penis. If they did, you would notice it right away, or shortly after using the condom. The main reaction that can occur is a latex allergy. This is where your skin will be come red and itchy shortly after using the condom. If this happens, then you should consider switching to a non-latex condom. There are many options available.
I should also mention that I applaud your use of condoms and I hope you continue to use them. They are the best way to prevent the spread of sexually transmitted diseases and are fairly good at preventing pregnancy. However, other forms of birth control
are more effective than condoms. This is important for you to know going forward. Condom use only prevents pregnancy about 90% of the time (which is good, but not perfect).
If you are having any trouble with them, you should schedule an appointment with your primary care physician
. He or she can help you find a brand or type that is better suited for you, if this issue comes up. Good luck.