I would suggest you contact your doctor if you are suffering from tendinitis.
NSAIDs are often used as part of treament for tendinitis, but like all medications they can have side effects. Therefore again if you have concerns about taking NSAIDs contact your doctor.
As for the mechinism of action of NSAIDs they don't constrict vessels but instead reduce the production of inflammatory mediators (prostoglandins) which act to dilate some vessels. These inflammatory mediators also make blood vessels more permeable so that nutrients and cells from the blood can pass through the vessel walls and carry out repairs to damage tissue. The problem however with the bodies inflammatory response is that it can be too severe, so that rather than providing healing it itself can cause damage and pain. For this reason (and many others) NSAIDs may be useful.
But again if you have concerns about taking NSAIDs or any medical condition these please consult your doctor. The internet is not an appropriate place for medical advice, your doctor is.