The trauma from previous experiences can make it extremely difficult to enter new relationships or to connect with someone new. It is not easy to be in a "functional" relationship when your trust has been broken or abused in the past. When you are healing from trauma, honor your feelings. It is okay to slowly build trust and have the people in your life earn it. Be kind and patient with yourself.
The first step to forming new relationships is assessing whether or not your future partner is worthy of your trust. Ask: Do they continuously do untrustworthy or hurtful things in your relationship? Do they have a pattern of acting in a way that causes you to question their character? If yes, consider whether that person is someone you should be working to trust. Seek an objective perspective from a loved one if you are having a hard time discerning if someone brings toxicity into your life.
If you are in a relationship currently, but it doesn't feel "functional," try to be open with your partner about how you are feeling. Giving context as to why it is difficult for you to trust within a relationship may give the other person more confidence to support you. Even a simple disclosure that "someone in the past harmed [you] causing [you] to want to take things slow" can help your new partner learn your needs. If they are not willing to respect your needs, that may be a sign that they might not be the appropriate partner for you at this time. Although another person can't complete the healing process for you, they can encourage you and assure you along the way.
This next part speaks to your question about shame. It is not uncommon to feel "dirty" or "ashamed" after experiencing sexual harm even though it was not your fault. You are not alone. Shame is a frequently cited emotional consequence of sexual violence, with one study noting that 75% of women sexual assault survivors indicated that they felt ashamed about themselves following their assault.
Shame thrives in silence. Learning about how society conditions survivors to feel ashamed can help empower you to recognize that abuse is never your fault, no matter what the circumstances. In addition, talking about your experiences and finding validation from trusted others can begin to decrease the shame you feel in every day life. You may want to also join groups where you can meet other survivors, as their stories and healing succuesses may give you the hope you need to keep going. Separate yourself from people who trigger your shame. You do not need them to cause you any additional pain.
Give yourself grace and honor your past feelings, but remind yourself that while your trauma may always be a part of you, you deserve a healthy and loving relationship external from that trauma. Face your shame head on, and surround yourself with supportive people who reinforce your worth and value. It does get better. Don't give up.