Yes, the symptoms you are experiencing could be due to anxiety/depression elicited by grieving. While it is normal to experience some of this during the grief process, if it goes on (consistently) for longer than a few months, worsens, and/or dramatically interferes with your ability to attend to your day to day life, it is important that you seek professional help. Certainly if you have thoughts of suicide, it is also important to seek help right away.
Many times a normal grief process can turn into a longer-standing depression, so it might be useful to monitor your symptoms closely and/or enlist the help of a friend or family member to tell you if they see things getting worse for you.
Some people find it helpful to seek counseling and/or a support group during grieving so as to have an outlet and a place to let out whatever emotions come up. Having this kind of outlet might help relieve some of your anxiety symptoms- usually anxiety occurs when we hold in emotions, so letting them out in a safe place/way might help.