Vaseline (petrolatum or ‘petroleum jelly’) is a hydrophobic and occlusive (air barrier) ointment that is not antimicrobial, and can potentially seal in anaerobic bacteria into a wound site. While your former girlfriend was wrong that wounds should be directly open to air, they should be capable of evacuating exudate (pus) and at least periodically exposed to oxygen to inhibit the growth of Staphylococcus bacteria, or else saturated in an antimicrobial ointment to inhibit bacterial growth. I’ve seen a lot of colloquial suggestions to use petroleum jelly to ‘seal’ a wound but I have not seen that recommended in medical literature and don’t carry Vaseline in my medkits, either for lacerations or burns. For punctures and lacerations I use an iodine solution and a topical antibiotic (or bandage with antibiotic solution) and for burns I use a surfactant burn gel.
As @Ulfreida notes, the imperative first step in wound treatment is irrigation and removal of any foreign debris, preferably with a syringe (without needle) or low pressure spray. Any water that you would drink is sufficient although a mild saline solution with a small amount of iodine solution is ideal, followed by a topical application of antibacterial ointment. Isopropyl alcohol, although useful for sterilizing instruments and injections sites, is not indicated for a wound site because it will cause inflammation and inhibit coagulation of platelets.
Following that, a cut with clean edges should be sealed together to promote healing, either by the use of butterfly closures or Steri-Strips®. If the wound is relatively shallow (only through the dermis) it can be covered with an occlusive dressing (preferably transparent so it can be inspected); this is particularly important in medical, food handling, or backcountry scenarios where exposure to pathogenic bacteria is frequently. If the wound is deep enough to require thread sutures then it should be covered with a removable dressing and a small section at one end upon to promote evacuation, and the patient evacuated to professional medical care as soon as possible. There are some specific procedures for closing deep wounds in the field without the use of thread sutures, which frankly if done without expertise can cause more problems than they reduce but in general if you have a deep wound that can’t be closed with adhesive bandages you need to seek medical care.
For minor abrasions and ‘clean’ lacerations, you shouldn’t have to replace bandages regularly because they should seal up with platelets quickly, forming an impermeable barrier to Staph and other micropathogens. For burns, application of burn gel and a loose dressing is recommended. For deeper wounds or with jagged edges, it is important to inspect the wound regularly for signs of infection, and respond to indications of sepsis promptly. One thing I learned in backcountry medical training is how seemingly minor injuries (particularly punctures and burns) can go from being minor irritants to major medical emergencies quickly if not promptly and correctly treated.
Stranger