Should i have my 3 yr old checked?

ive had it suggested to me by 2 different people to have him checked by a doctor to see if theres something going on other than typical 3 year old behavior, my 3 year old will zone out while he is eating and sit there with the same piece of food in his mouth not chewing or anything for several minutes and when i call his name he jumps as if startled and will chew a few times and do the same thing again, the last bite of food hell let sit in his mouth for a long time and refuse to swallow it, he will not make eye contact, he has extreme tantrums, some of them lasting up to 3 hours at a time or more, he doesnt seem to understand when i tell him he can have something in a little while but not right now or if i tell him if he doesnt do xx he cant have xx or hell have xx taken away, last night he got out of bed 5 times during the night turned his light on and sat in the middle of his floor, when i tried putting him back in bed he started screaming and trying to kick me, when he is in his room throwing a tantrum hell scream at the top of his lungs, bang on the walls and door, run into the door from across the room, jump up and down, etc. he has at least 3 tantrums a day, sometimes the smallest thing will set him off and it will do on for hours, sometimes hell stop for 10 mintues and than start right back up with the tantrum, he repeats himself a lot like today in the store he kept repeating he wanted milk and i told him he had to wait until we got home because i didnt have any with me (he had a drink right before we left and we were only gone about 30-45 minutes) and i tried ignoring him, and he just kept saying he wanted a drink the entire time we were gone, hes never thrown a tantrum or misbehaved in public with me before today, every time i told him he had to wait until we were done he started crying and getting louder repeating his question. after we got home he had a drink and i told him to go play for a little while so i could put things away and than he could have another drink and snack as long as he could behave and he went into his room and threw himself on the ground screaming saying "go get me milk right now." he doesnt like playing by himself ever, not even for a few minutes, and he tells me he doesnt want to play. theres probably a ton i missed but i talked to a social worker recently and some of these things came up and she seemed concerned, and i talked to someone else who said they think i may need to have him evaluated... im so confused, and stressed and tired, we have had 2 weeks non stop of this, and im at the end of my rope.