Torn Urethra from peeing??🤔

Good evening ladies. So here’s what’s happening. I currently have a cold and I’m at work (I’m a nanny for a family i trust so it sit on their toilet) and i have the urge to go pee which is normal and all. So i go pee and I’m peeing everything is fine then i have this feeling in my chest that i feel like i have to cough. I’m sick so I’ve been coughing a lot. So i cough really hard while I’m peeing then BOOM!! I get this super stinging feeling and it hurts so bad that i literally jump off the toilet! Like i literally jumped up because the pain was so bad. It felt like a sting. So I’m like wtf and i open my legs to look down at the toilet and i saw blood dripping. So i wipe and it’s a little red and pink spots on the tissue. And that was like 4 hours ago and now I’ve peed about 3 times sense them which is also Kemal for me because i drink a lot of tea lol and every time since then it stings a little and it’s a little bloody.

So my question is do you think the pressure of my cough that made me push a little bit caused my pee to come out so fast the it tore my urethra a little bit? Because that’s all i can think of because i know for a fact that’s it’s not a uti because i was peeing normal with no pain then right in the middle of my pee stream coming out i cough really hard then all the pee just squirted out really fast causing my

Urethra to rip or stretch maybe? Idk has this happened to anyone before? can anyone make sense of it? If so do you think it will heal on it’s own or should i go to the doctor. I don’t feel any pain other than those first 3 seconds when the per first comes out and when it comes out i pee for a long time so it’s no uti. Ugh it’s just annoying seeing the blood and stings for the first 3 seconds of me peeing.