The website link below is all about beach hazards. This will help you to identify what plant or creature you are coming into contact with. Best thing to do is to avoid it.
http://www.gmanetwork.com/news/story/306524/lifestyle/healthandwellness/first-aid-tips-for-jellyfish-stings-and-other-beach-hazards
A dermatologist (skin doctor) specialises in diseases of the skin or skin disorders that persist for a long time. Having some spikes stick into the skin, does not warrant a visit to a skin specialist. If there was a problem, the first person to see would be your own doctor who would refer you to a specialist if this was deemed necessary.
I suggest go to a skin doctor
You do not say where the beach is, nor which part of the body these spines get stuck into. There may be some creatures there that you cannot see and then get their spines stick into you.
You either need to avoid going to the beach or wear protective footwear and clothing so as not to get the spines to stick into you.
You are doing the right thing in pulling them out with the tweezers. You can also apply some antiseptic cream when you have plucked these out. You can buy antiseptic cream from your pharmacy.