Rash and Blisters on Skin Above Upper Lip After Juvederm Injections?

Lip injections can trigger a herpes breakout (cold sore) even if you never had one before. A herpes outbreak lasts approx 14 days. The antiviral medication, Acyclovir helps stop viral shedding and may even prevent a breakout in the future if caught in time.  The nerves in that area may tingle and ache but this should resolve in a couple of weeks.  You may want to try a different ointment as neosporin has been known to cause an allergy for some people. This can be an irritant too  

Herpes Simplex Virus 1 (HSV1) is a common condition with symptoms that include burning rashes, and blisters. The virus lies dormant leaving some patients unaware they are carriers. HSV1 can be reactivated by an injury, including lip injections. It is best to follow up with your injector to rule out the possibility of an allergic reaction.
Discuss taking anti-viral medication with your physician prior to your next lip injection. This may lessen the chance of reoccurrence. 

Sounds like an outbreak of cold sores, which is not unusual after lip injections. Take the medication prescribed and you may need a couple rounds of anti-viral if the outbreak bad. 

Herpes eruptions can be triggered by lip injections. Any trauma to the area where cold sores (herpes) have occurred can potentially trigger an eruptions. One way to prevent these is to give antiviral medications, such as valcyclovir or famcyclovir, prior to lip injections.

It's also important to note that Neosporin can cause allergic reactions, so the burning may be from the herpes (which can last several days) or from an allergic reaction to Neosporin.  I recommend that you stop Neosporin.  If the burning continues longer than one week after the blisters have healed, please consult your injecting physician to determine the cause.

I believe your doctor is correct that this represents a herpetic eruption and the treatment is appropriate.  You should have no long term problems and it sounds like it is well on its way to healing.  Definitely should pretreat with an antiviral like Valtrex before any future fillers or other facial procedures..