Treatment for Horizontal Line Under the Eyes?

This area can be managed
either with Botox or, if the wrinkles are deep, you can do laser skin resurfacing.

It seems that you are noticing either 'tear trough' line or festoons of the lower eyelids.
Either case you have the option of either getting a filler to fill up the groove or injecting a small amount of Botox to relax the hyperactive lower eyelid muscle causing the line.
Surgical options will work well by removing any excess fat from the lower eyelid.
Regards

The horizontal wrinkles underneath the eyelids can be addressed through a pinch technique on the lower blepharoplasty. This is usually done in conjunction at the same time as the fat removal from the lower lids. The incision for the lower lids is made after a lash line and is nearly invisible within a month after the procedure. This usually gets rid of lines close to the lash line, but if the wrinkle is more than a quarter of an inch below the lash line it may not be able to be removed.

The deep line that you're describing sounds to me like your lid/cheek junction. This occurs at the lower orbital rim. It is accentuated by pseudoherniation of fat in the lower lids (bags) and descent of the cheek fat. Smiling will make it worse. Fixes can be temporary such as with fillers-Radiesse is good for this. Fat can be useful as well. But likely you are headed toward lower lid surgery and/or surgery for cheek elevation.

Is the line a contour problem or a crease in the actual skin? Irish skin, due to its fairness, can exhibit premature aging with wrinkling and thinning. If the line is cause by loss of elasticity, a peel of sorts, chemical or laser, might be just what the doctor ordered.