Our members have patiently answered you that you had no risk.
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Since you had protected sex, we are telling you emphatically, you had no risk. You'd know if the condom broke, it's time to move let your fears go.
Lambskin doesn't prevent hiv transmission which is one reason why sex workers don't use them.
Just to expand this a bit, coconut oil can damage latex condoms. If you're using a different type of condom, coconut oil won't damage them. The virtue of latex is it's stronger and stretches better than other materials. But some are allergic to latex and some just don't plain like it, as it's pretty thick. Other materials such as lambskin, polyurethane, etc. are thinner and therefore feel better during sex but are more prone to breaking, though usually they won't, and to slippage. As for the health of the vagina, the evidence is not clear. Coconut oil is claimed to be antibacterial, but it really isn't all that much, but it is somewhat anti-fungal, so that makes it at the same time healthy as it might prevent or limit yeast infections but it might, though this isn't proven, cause some disruption of beneficial flora that lives in the vagina. I wouldn't personally use it, as it's really thick and you have to use virgin oil which can go bad if you don't keep it refrigerated, but if you just put oil for lube on the outside of the vagina where you actually need it for entry it's probably not a problem. But as noted above, don't use with latex condoms, the ones that are best at preventing what you use condoms to prevent. Personally, when I've used condoms, I've used the lambskin and the thin ones, as I like to feel what I'm doing, and I've never had a problem. But it is more labor intensive as you have to make sure it stays on and doesn't break. Anyhoo, just sayin;.
Using coconut oil is a bad idea - it's not intended for use on genitals, and it can weaken a condom and cause it to break. Fortunately, your condom did not break. You would have noticed if your condom broke - it is impossible to miss that.
So, you had no risk for HIV.