My neck pulse feels like its swooshing and vibrating. Should I get it checked out?

Yes. As long as you have no stroke symptoms or vision changes, can see pcp if soon. Will listen for bruit and possibly order ultrasound of carotids. Concern is for blockage or dissection/aneurysm. If have stroke symptoms or history call for ambulance. Also helpful to check your BP and make sure is not at dangerous level. When in doubt, check it out.
Absolutely. The simplest test for this is a carotid ultrasound. This a noninvasive test that can be simply done to identify if there are any blockages in the carotid arteries.