New vein formation after sclerotherapy does happen and usually resolves on its own over about a one year period. This is called matting when it consists of very tiny vein formation. Larger vein formation is sometimes called neovascularization. When either of these occur, I usually treat them at the next session of sclerotherapy. Matting does respond to glycerine injections or sometimes to finding a feeding vessel. Neovascularizaton will usually respond to more sclerotherapy or a higher dose. Follow up with your treating physician and remember that sclerotherapy is a process over time.
Telangiectatic matting after sclerotherapy
Telangiectatic matting after sclerotherapy is well described and these very small (smallest of the capillaries) are very fragile and the literature shows that they will resorb on their own within 12 months. Telangiectatic matting also occurs after topical laser treatment for spider and reticular veins.