First, glad your OK.

That out of the way if it happened in my house the priorities would be different.

Slice myself open on a window and it will be my immediate duty to jump through said window. A laceration might possibly kill me but if I bleed on her carpet the lady of the house will surely kill me. Don't care if it is the fourth floor. You have to suck it up and keep your priorities straight. Jumping also puts you on the ground floor and closer to where the ambulance will be. Saves the EMTs work. That is the second priority: Don't [censored] off the EMTs. If they like you they might even stop to put you out at the emergency room. Drive-by deliveries, Gurney kicked out as they make the corner on the way to the doughnut shop, are both more entertaining and painful.

Remember that at home the lady of the house holds your life in her hands. And on the way to the ER the EMTs have you by the short and curlies. Keeping on the good side of the lady of the house and EMTs is an important survival strategy. One not often mentioned. A word to the wise.

More seriously those bandages usually work more quickly if you apply firm pressure for the first few minutes. They tend to soak through more quickly when just laid on or released too soon. Of course you may have been applying plenty of pressure but you had sliced a minor vessel. Everyone's mileage varies. Two seemingly identical wounds. One barely bleeds a drop while the second looks like a prop in a cheap slasher film, blood for days.

A trauma bandage is good but they have to be applied fairly tight. Most people try to hold one tail on their teeth and pull the other end with the free hand. It can work but a stronger move is to kneel and catch one end under a boot or knee. The free hand grabs the other end. Straightening up allows you to use your whole body to get an effective pull to draw it up firmly.

An ACE bandage over a 5by9 surgical bandage is a good substitute. Precut tape speeds one handed application. A piece or two to hold the pad. Another at the end of the ACE and wind. Finish with another piece or two. Firm pressure.

What even happened to men having a handkerchief. I carry a clean, folded cotton bandanna. That way you always have a dressing, field expedient filter mask, etcetera. Always amazes me the number who don't. That said it might not have helped. Sometimes I forget I have one.

In a pinch a bandanna makes a reasonably good bandage and most athletic socks have enough elastic to act as a expedient, if someone short, ACE bandage. Not perfect but something to keep in mind.

You lived. So you obviously did something right. Now if we could just get an international team of anger management and conflict resolution negotiators to get between you and the fenestration...