It sounds as if your muscle around the eye is strting to compensate for the areas being restricted. It can feel very "tired" at first, but usually this is temporary. give it another week. Then you could consider Botox to the lower lid region if you are a good candidate.
Botox does not cause wrinkles but often times wrinkles in the areas adjacent to the area that you treated become more noticeable when the treated area is smoother. Sometimes this is referred to as "compensatory wrinkles". The filler may or may not be required but I can't tell without a physical exam. Adding a little more Botox in the area where there are wrinkles will most likely be helpful. Botox and its competitor's are not miracle drugs but they are very effective. Often times patients noticed these adjacent areas of wrinkles after treating their crows feet or from lines. It's a little bit like updating the kitchen then noticing how bad the living room looks.
Just go slowly and be conservative. Remember, having someone who injects Botox in a way that you enjoy is a little bit like finding a stylist who really knows your face and your hair. Everyone will inject Botox a little bit differently
Botox does ot actually cause new wrinkles, what you are seeing are wrinkles that are called compensatory wrinkles. These result from inactivity of some muscles while the untreated muscles become more prominent or noticeable. Sometimes there is not way to treat these, but oftentimes some minor Botox touch up will improve the "new wrinkles".
Joe Niamtu, III DMD
You should go back to the dermatologist who did the Botox and get more Botox in the areas that most probably were not treated and now are compensating for the inactivity of the treated areas. That happens often if the frown is treated and the base of the nose is not, and if the crows feet are treated and under the eys are not.
It is very common especially under the eyes to occasionally have new wrinkles that form as your body compensates for the decreased motion in one area ftom Botox it can rev up another area. A bit more Botox almost always solves this issue but it is patient dependent so speak to your doctor.