Am I obligated to go to the mikvah if my husband does not want to have relations?
Yes, you should still go to the mikva, even though you won’t have relations with your husband. From a halachic angle, going to the mikva will allow handing things to each other, and other forms of contact aside from relations.
Secondly, for your shalom bayis. No matter what happens in the marriage, we continue to act as normal as possible. Not going to the mikva, places a wedge between the two of you, which is unhealthy, and just adds fuel to the fire, and complicates things.
If you would like to talk to someone about your marriage let me know and I can give some suggestions.