Should I seek medical help for metal puncture?

Bruising and discomfort after sclerotherapy are natural which normally resolves within a few days. But since you said your veins look worse and are more visible after the procedure could indicate a complication. It's good that you have already spoken with your doctor, but still experiencing discomfort or have any concerns, follow up with them promptly. 

In some cases the veins may fade on their own over time, but if the issue is related to the sclerotherapy procedure, additional treatment can be needed. Its best to follow up with your doctor to discuss your options and determine the best treatment.

Your face might seem burnt from too much exposure to the sun, and this can be very uncomfortable. This occurs when the skin gets too much sun without protection. Symptoms can be redness, pain, and maybe blistering. Immediately get into the shade for relief, apply a cool compress, and use aloe vera gel to soothe. Wear sunscreen in future to avoid a repeat of the same.

It advisable to wait 4 weeks after the vaccination to avoid any infection.
 

Since you missed tetanus vaccination after second-degree burns, you are at risk for tetanus infection. The symptoms may be visible within 3 to 21 days, usually at 7 to 10 days. Tightness of muscles, spasms in the jaw, and difficulty in swallowing are some of the symptoms that one may experience. If you notice these signs, you should seek medical attention at once. The tetanus vaccine can, however, be administered after an injury to avoid infection.