There are a variety of products, both prescription and over the counter, available for the treatment and prevention of cold sores. Many of the products you listed in your question are only beneficial for the symptoms of cold sores and won't improve healing time. Below, we list 3 of the most beneficial products for cold sores.
You mentioned you have used this before, but it is worth putting here. As an over the counter product, it is easily accessible and has evidence for benefit. It does not immediately kill the herpes simplex virus (the virus that causes cold sores) but prevents viral replication, which very often reduces the healing time when an outbreak occurs. Most studies show that Abreva reduces the healing time by an average of 4.6 days versus placebo.
So while Abreva won't make a cold sore go away immediately, it should make it heal faster. Be sure that you are applying the product correctly. It should be applied 5 times daily beginning as soon as symptoms begin. The earlier the treatment with Abreva begins, the more effective it will be. If you have any hint of a red spot forming or mild pain on your lip, begin using the product.
These are prescription antivirals and are most likely the quickest and most effective treatment available. If you have recurrent outbreaks or particularly painful ones, ask your doctor about these antivirals.
Acyclovir is available as both an oral capsule and a topical ointment. When taking the oral product, it needs to be dosed 3 to 4 times daily as soon as symptoms start. The topical product, which also goes by the brand name Zovirax, needs to be applied 5 to 6 times daily for 7 days. The topical product isn't used all that often as it typically is very expensive and seems to work no better than the oral product.
Valacyclovir is only available as a tablet. Valacyclovir is very similar to acyclovir but only needs to be dosed 2 times daily so it is more convenient to take.
For a natural remedy, lysine has a lot of evidence for use in the treatment/prevention of cold sores and is certainly an option if you do not want a prescription antiviral.
Multiple studies have shown that lysine, when used in doses of 1,000 mg to 3,000 mg daily, is effective for preventing recurrent episodes of cold sores. It is important to note that the most positive evidence for Lysine is when it is used as a prophylactic. If you are having constant recurring problems, it is often recommended to use lysine daily as a supplement. Not only can this prevent episodes from happening, it may lessen the severity if they do happen.
That isn't to say lysine isn't an effective treatment for an active infection. Many studies have shown that it can improve healing time, it just may not be as effective as Abreva or the prescription options.
You also have the option of applying lysine topically. One study showed that the topical application of one specific product (Super Lysine Plus +) was helpful in improving healing time from an active infection. In fact, 87% of participants had full resolution in only 6 days! The specific product used in the study reference contains lysine in addition to a variety of other ingredients.
So, as you can see, you have many options. If you want to try a more natural remedy, lysine has some positive evidence. You may try supplementing daily with lysine and use a topical lysine product if an outbreak occurs. If you find lysine not working well, a prescription antiviral may be your best choice.
Be sure to talk to your doctor regarding your treatment options.