What is the biblical basis against seeking medical advice? Which scriptures are used to deter Christians from seeking medical advice or the help of a doctor?
The overwhelming majority of Christians, based on their understanding of the Bible, see nothing wrong with seeking medical advice and help.
There are, however, a few passages which may deter people from seeking medical advice.

And Asa in the thirty and ninth year of his reign was diseased in his feet, until his disease was exceeding great: yet in his disease he sought not to the LORD, but to the physicians. 2 Chronicles 16 12
Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord:James 5 14

In the first of these Asa sought the help of physicians but did not pray about it. In the next verse he died. In the second, prayer is recommended in the case of sickness.
These verses could be seen as saying that prayer is the best response to sickness. It is what Asa omitted to do, and what James urges his readers to do. There is no suggestion, in the text,  that Asa was wrong to seek the help of physicians, or that James was saying that prayer alone is needed. Some however have seen an either/or dichotomy here. Adherents of the Christian Science movement have traditionally held this view. Should we pray or should we go to the doctor? A relevant text in considering this possible dichotomy, if it exists at all, is:

Jesus answered him, &quot;It is also written: 'Do not put the Lord your God to the test.'&quot; Matthew 4 7

Any idea of avoiding medical help with the intention of seeing whether God will  perform a miracle, seems condemned here.
Another verse is worth mentioning here. It  concerns a lady who had been unwell for twelve years:

And had suffered many things of many physicians, and had spent all that she had, and was nothing bettered, but rather grew worse. Mark 5 26

This may deter some, or at least act as a cautionary tale, to be on our guard. Modern professional regulation may provide some assurance on this issue.
Finally there are some treatments which may be considered forbidden or unethical. Jehovah's Witnesses do not condone blood transfusion, for example. Also, many Christians consider abortion a sin and so requesting medical help to end a pregnancy would be considered wrong and counter to the commandment not to kill.