Important to address allergies first, and have transconjunctival blepharoplasty only if puffiness remains
As a cosmetic oculofacial plastic surgeon, I deal with many patients who have an allergic conjunctivitis history. The first thing I recommend before considering any surgical procedure is the management of the allergies because allergic conjunctivitis will cause swelling and puffiness to the eye area even with the reduction of fat. If there’s puffiness that’s related to fat prolapse, which is fat that’s normally behind the eye pushing forward also called fat herniation, then that can be addressed surgically. However, if the goal is to reduce puffy bags from the eyes, then we should try to manage it from all angles. So meet with your doctor whether it’s your ophthalmologist or allergist to get on the right regimen of antihistamines, eye drops and even nasal sprays if there’s a rhinitis component to this and try to get that under control.
After the allergies are under control, and you still have bulging of fat that’s pushing forward, the most common procedure that I recommend for someone who’s young, dark skinned and who has fat prolapse is transconjunctival blepharoplasty. This procedure is the reduction and sculpting of fat from the inside of the eyelid, so there’s no scar on the outside. When you’re young and you have dark skin, you’re likely to show an incision even if it’s done finely and beautifully, and we want to avoid it. So, I perform transconjunctival blepharoplasty routinely in my younger patients with darker skin types to assist them in reducing the area of puffiness.
After eyelid surgery, I encourage my patients to still manage their allergies because seasonal allergies and other things can still affect the final aesthetic result of the eyelid surgery. The surgery can correct the fat prolapse but the management of the allergies is also critically important for the long-term aesthetic of the eyes.
Blepharoplasty vs fillers
There should not be a difference between the two with regards to your allergic conjunctivitis. Your allergy is to environmental allergens and there should be no issue with fillers with that regard.
However, when ever your do a procedure, surgical or otherwise, swelling will occur, and if you are suffering from the allergies at the same time, it could prolong healing time.
Your best bet is to have the procedure during a time [season] where your allergies are not acting up, and use anti-allergy medications as a precaution when having the surgery or procedure.
Tear trough and upper cheek fillers
Yes, I think that you would be best with a very small amount of Restylane into the area just between the cheek and the tear trough where the bone is quite flat and there is not much soft tissue. I would start with just 1 ml Restylane done by canula. That is the least invasive and also enables deep delivery of the filler where it will build up the volume but not "show". The idea is to gently build up the cheek below the eyes and in the nasojugal line (an oblique depression on the cheek extending down from the tear trough). I would advise against filler directly into the tear trough and against transconjunctival blepharoplasty as you are quite young and filler may well achieve the subtle result you want with much less down time. It is also reversible with injection of hyalase enzyme.
I would recommend treating the allergic conjunctivitis completely and evaluating your eyes again when the allergies are not active. I like to start with over-the-counter allergy eye drops such as Zaditor, as well as an oral antihistamine such as Claritin. It is difficult to recommend a procedure without examining you in person, but it looks like there is severe hollowing in the lower eyelids and upper cheeks. I suspect you could benefit from filler injections in this area.